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All questions of Squaring, Exponents and Square Roots for ACT Exam
How many natural numbers lie between 92 and 102?
a) 36
b) 27
c) 9
d) 18
Correct answer is option 'D'. Can you explain this answer?
|
Sohini Das answered |
Between 92 and 102
Here, n = 9 and n + 1 = 10
∴ Natural number between 92 and 102 are (2 × n) or 2 x 9, i.e. 18.
Here, n = 9 and n + 1 = 10
∴ Natural number between 92 and 102 are (2 × n) or 2 x 9, i.e. 18.
Which of the following is a perfect square number?
- a)222222
- b)23453
- c)1681
- d)1057
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a perfect square number?
a)
222222
b)
23453
c)
1681
d)
1057
|
Shashwat Singh answered |
The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.
Find the perfect square number between 30 and 40.
- a)36
- b)49
- c)25
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Find the perfect square number between 30 and 40.
a)
36
b)
49
c)
25
d)
none of these
|
Amita Verma answered |
Since, 1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
Thus, 36 is a perfact square number between 30 and 40.
Which of the following would end with digit 1?- a)1232
- b)1612
- c)772
- d)822
Correct answer is 'B'. Can you explain this answer?
Which of the following would end with digit 1?
a)
1232
b)
1612
c)
772
d)
822
|
Sneha Singh answered |
Option B is correct because the unit digit of 161 is 1 and if unit digit of any digit ends with 1 the its square will also end with 1.
Without doing any calculation, find the numbers which are surely perfect squares.- a)441
- b)408
- c)153
- d)257
Correct answer is option 'A'. Can you explain this answer?
Without doing any calculation, find the numbers which are surely perfect squares.
a)
441
b)
408
c)
153
d)
257
|
KS Coaching Center answered |
The perfect squares have 0,1,2,4,5,6 or 9 at their units place.
Therefore153,257 and 408 are surely not perfect squares.
Therefore153,257 and 408 are surely not perfect squares.
Without adding, find the sum. 1 + 3 + 5 + 7 + 9 + 11 + 13
- a)36
- b)49
- c)25
- d)19
Correct answer is option 'B'. Can you explain this answer?
Without adding, find the sum. 1 + 3 + 5 + 7 + 9 + 11 + 13
a)
36
b)
49
c)
25
d)
19
|
Zzz answered |
We have to just add that how many odd no. are there then we have to take out
Without adding, find the sum. 1 + 3 + 5 + 7 + 9- a)16
- b)36
- c)9
- d)25
Correct answer is option 'D'. Can you explain this answer?
Without adding, find the sum. 1 + 3 + 5 + 7 + 9
a)
16
b)
36
c)
9
d)
25
|
|
Kiran Mehta answered |
Here, we have to find the sum of first five odd natural numbers.
Therefore, 1 + 3 + 5 + 7 + 9 = (5)2 = 25
Find the least number that must be subtracted from 5607 so as to get a perfect square.- a)130
- b)135
- c)131
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Find the least number that must be subtracted from 5607 so as to get a perfect square.
a)
130
b)
135
c)
131
d)
none of these
|
Sounak Sengupta answered |
Square of 75 is 5625
square of 74 is 5476
so use must get 5476
5607 - x is 5476
x is 131
square root of 5476 is 74
What is the least perfect square which is divisible by 2, 4 and 6?
- a)36
- b)64
- c)16
- d)18
Correct answer is option 'A'. Can you explain this answer?
What is the least perfect square which is divisible by 2, 4 and 6?
a)
36
b)
64
c)
16
d)
18
|
Preeti Khanna answered |
LCM of 2,4,6= 2×1×2×3=12
Least perfect square which is a multiple of 12 is 36.
Least perfect square which is a multiple of 12 is 36.
22 x 23 x 24 is equal to:- a)224
- b)2-5
- c)29
- d)2-9
Correct answer is option 'C'. Can you explain this answer?
22 x 23 x 24 is equal to:
a)
224
b)
2-5
c)
29
d)
2-9
|
|
Ayesha Joshi answered |
By laws of exponents:
am x an = am+n
22 x 23 x 24 = 22+3+4 = 29
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Squares and Square Roots, Class 8, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.Q.Which of the following is a perfect square number?- a)222222
- b)23453
- c)1681
- d)1057
Correct answer is option 'C'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Squares and Square Roots, Class 8, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.
Q.
Which of the following is a perfect square number?
a)
222222
b)
23453
c)
1681
d)
1057
|
|
Kavya Saxena answered |
The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.
If a number has 1 or 9 in the unit’s place, then it’s square ends in ________.
- a)3
- b)9
- c)1
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If a number has 1 or 9 in the unit’s place, then it’s square ends in ________.
a)
3
b)
9
c)
1
d)
none of these
|
Rajeev Kumar answered |
If a number has 1 or 9 in the unit’s place, then it’s square ends in 1
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Squares and Square Roots, Class 8, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.Q.Which of the following is a perfect square number?- a)222222
- b)23453
- c)1681
- d)1057
Correct answer is 'C'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Squares and Square Roots, Class 8, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.
Q.
Which of the following is a perfect square number?
a)
222222
b)
23453
c)
1681
d)
1057
|
Sanjana Bose answered |
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 1681 is 41.
Therefore, the square root of 1681 is an integer, and as a consequence 1681 is a perfect square.
As a consequence, 41 is the square root of 1681.
None of the square numbers end with _________ at unit’s place.
- a)3
- b)2
- c)7
- d)2, 3, 7 or 8
Correct answer is option 'D'. Can you explain this answer?
None of the square numbers end with _________ at unit’s place.
a)
3
b)
2
c)
7
d)
2, 3, 7 or 8
|
|
Preeti Khanna answered |
According to the Property 1, A number having 2, 3, 7 or 8 at it's unit's place is never a perfect square. In other words, no square number ebds in 2, 3, 7 or 8.
How many numbers lie between square of 12 and 13- a)22
- b)23
- c)24
- d)25
Correct answer is option 'C'. Can you explain this answer?
How many numbers lie between square of 12 and 13
a)
22
b)
23
c)
24
d)
25
|
|
Rhea Reddy answered |
122 = 12*12 = 144
132 = 13*13 = 169
Now numbers are between144 and 169 are:
145, 146, 147,.............168
Total number = 24
So total numbers lies between 144 and 169 is 24
If 5278 is squared, then what will be at unit place?- a)4
- b)7
- c)6
- d)8
Correct answer is option 'A'. Can you explain this answer?
If 5278 is squared, then what will be at unit place?
a)
4
b)
7
c)
6
d)
8
|
Trisha Vashisht answered |
When squaring the number 5278, the unit digit is determined by the square of the unit digit of the original number.
Since the unit digit of 5278 is 8, squaring it gives 8 × 8 = 64.
Therefore, the unit place digit of 5278² is 4.
Therefore correct answer : Option A
Therefore correct answer : Option A
2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of plants in each row.
- a)55
- b)65
- c)45
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of plants in each row.
a)
55
b)
65
c)
45
d)
none of these
|
|
Rajeev Kumar answered |
Let the number of rows be x
Thus, the each row contains x plants.
The total number of plants in the garden = number of rows × number of plants in each rows
Thus,
2025=x×x
=>x2 =2025
=>x= 3×3×3×3×5×5
=3×3×5
=45
Thus, there are 45 rows and each row contains 45 plants.
Thus, the each row contains x plants.
The total number of plants in the garden = number of rows × number of plants in each rows
Thus,
2025=x×x
=>x2 =2025
=>x= 3×3×3×3×5×5
=3×3×5
=45
Thus, there are 45 rows and each row contains 45 plants.
What is the value of 42 x 4-2?- a)16
- b)8
- c)1
- d)0
Correct answer is option 'C'. Can you explain this answer?
What is the value of 42 x 4-2?
a)
16
b)
8
c)
1
d)
0
|
Orion Classes answered |
42 x 4-2
By law of exponents:
= 42+(-2) = 42-2 = 40 = 1
57/67 will give the value:- a)(⅚)7
- b)(⅚)0
- c)(⅚)-7
- d)(6/5)-7
Correct answer is option 'A'. Can you explain this answer?
57/67 will give the value:
a)
(⅚)7
b)
(⅚)0
c)
(⅚)-7
d)
(6/5)-7
|
|
Ayesha Joshi answered |
By exponent law:
am/bm = (a/b)m
57/67 = (⅚)7
Find the perfect square numbers between 50 and 60.
- a)64
- b)49
- c)no number
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Find the perfect square numbers between 50 and 60.
a)
64
b)
49
c)
no number
d)
none of these
|
|
Anita Menon answered |
Since we have 72=49 and 82=64. And both numbers lies outside 50 and 60 There is no perfect square between 50 and 60.
865000 is equal to:- a)8.65 × 105
- b)8.65 × 103
- c)8.65 × 106
- d)8.65 × 104
Correct answer is option 'A'. Can you explain this answer?
865000 is equal to:
a)
8.65 × 105
b)
8.65 × 103
c)
8.65 × 106
d)
8.65 × 104
|
|
Ayesha Joshi answered |
865000 is equal to 8.65 × 105
Find the square root of 529.
- a)24
- b)23
- c)25
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Find the square root of 529.
a)
24
b)
23
c)
25
d)
none of these
|
|
Rajeev Kumar answered |
Square root of 529 is 23
The multiplicative inverse of 1/32 is:- a)3-2
- b)32
- c)3
- d)⅓
Correct answer is option 'B'. Can you explain this answer?
The multiplicative inverse of 1/32 is:
a)
3-2
b)
32
c)
3
d)
⅓
|
|
Ayesha Joshi answered |
The multiplicative inverse of 1/32 is 32.
1/32 x 32 = 1
What will be the number of zeros in the square of 60?
- a)1
- b)2
- c)3
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
What will be the number of zeros in the square of 60?
a)
1
b)
2
c)
3
d)
none of these
|
Samridhi Patel answered |
Square of 60 is 3600 therefore number of zeroes is 2.
32 x 42 is equal to:- a)121
- b)49
- c)144
- d)156
Correct answer is option 'C'. Can you explain this answer?
32 x 42 is equal to:
a)
121
b)
49
c)
144
d)
156
|
|
Orion Classes answered |
By exponent law;
am x bm = (ab)m
32 x 42 = (3×4)2 = 122 = 144
The value of 2-2 is:- a)4
- b)¼
- c)2
- d)½
Correct answer is option 'B'. Can you explain this answer?
The value of 2-2 is:
a)
4
b)
¼
c)
2
d)
½
|
Suman Rajput answered |
The multiplicative inverse of 7-2 is:
A. 72 B. 7 C. 1/72 D. 1/7
A. 72 B. 7 C. 1/72 D. 1/7
Find the greatest 4-digit number which is a perfect square.- a)9990
- b)9801
- c)9999
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Find the greatest 4-digit number which is a perfect square.
a)
9990
b)
9801
c)
9999
d)
none of these
|
|
Kavya Saxena answered |
By division method we find the root of 9999 and we get the remainder 198.So subtracting 198 from 9999 we get 9801 as the greatest 4-digit perfect square.
1000 + 200 + 50 is equal to- a)125
- b)25
- c)1/125
- d)3
Correct answer is option 'D'. Can you explain this answer?
1000 + 200 + 50 is equal to
a)
125
b)
25
c)
1/125
d)
3
|
Bella Clarke answered |
Explanation:
To solve this problem, we need to determine the value of the expression 1000/200/50.
Step 1: Division
We start by performing the division operation. Dividing 1000 by 200 gives us 5.
1000 ÷ 200 = 5
Step 2: Division
Next, we divide the result from step 1 by 50. Dividing 5 by 50 gives us 0.1.
5 ÷ 50 = 0.1
Step 3: Simplify
We can further simplify the expression by expressing 0.1 as a fraction. Since 0.1 is equivalent to 1/10, we can rewrite the expression as:
1/10
Step 4: Simplify
Finally, we simplify the fraction 1/10. We can do this by multiplying the numerator and denominator by 10. This gives us:
(1 × 10) / (10 × 10) = 10/100
Simplifying further, we divide both the numerator and denominator by their greatest common divisor, which is 10:
10 ÷ 10 / 100 ÷ 10 = 1/10
Conclusion:
Therefore, the expression 1000/200/50 is equal to 1/10, which is option 'D'.
To solve this problem, we need to determine the value of the expression 1000/200/50.
Step 1: Division
We start by performing the division operation. Dividing 1000 by 200 gives us 5.
1000 ÷ 200 = 5
Step 2: Division
Next, we divide the result from step 1 by 50. Dividing 5 by 50 gives us 0.1.
5 ÷ 50 = 0.1
Step 3: Simplify
We can further simplify the expression by expressing 0.1 as a fraction. Since 0.1 is equivalent to 1/10, we can rewrite the expression as:
1/10
Step 4: Simplify
Finally, we simplify the fraction 1/10. We can do this by multiplying the numerator and denominator by 10. This gives us:
(1 × 10) / (10 × 10) = 10/100
Simplifying further, we divide both the numerator and denominator by their greatest common divisor, which is 10:
10 ÷ 10 / 100 ÷ 10 = 1/10
Conclusion:
Therefore, the expression 1000/200/50 is equal to 1/10, which is option 'D'.
What is the value of (22 + 32 + 42)0?- a)9
- b)0
- c)1
- d)14
Correct answer is option 'C'. Can you explain this answer?
What is the value of (22 + 32 + 42)0?
a)
9
b)
0
c)
1
d)
14
|
Scarlett Reed answered |
Value of (22 32 42)0 is 1.
Explanation:
To solve this problem, we need to understand the concept of exponentiation and the rules that govern it.
Exponentiation is a mathematical operation that involves raising a base number to a certain power or exponent. In this case, the base number is (22 32 42) and the exponent is 0.
When we raise any number to the power of 0, the result is always 1. This is a fundamental rule of exponentiation.
To understand why this is the case, let's break down the expression (22 32 42)0:
- The expression inside the parentheses, 22 32 42, represents the multiplication of these three numbers.
- In this case, 2 * 2 * 3 * 3 * 4 * 4 equals 576.
- The expression 576 raised to the power of 0 means we are multiplying 576 by itself 0 times.
- Since any number multiplied by itself 0 times is always 1, the result of (22 32 42)0 is 1.
In summary, the value of (22 32 42)0 is 1.
Explanation:
To solve this problem, we need to understand the concept of exponentiation and the rules that govern it.
Exponentiation is a mathematical operation that involves raising a base number to a certain power or exponent. In this case, the base number is (22 32 42) and the exponent is 0.
When we raise any number to the power of 0, the result is always 1. This is a fundamental rule of exponentiation.
To understand why this is the case, let's break down the expression (22 32 42)0:
- The expression inside the parentheses, 22 32 42, represents the multiplication of these three numbers.
- In this case, 2 * 2 * 3 * 3 * 4 * 4 equals 576.
- The expression 576 raised to the power of 0 means we are multiplying 576 by itself 0 times.
- Since any number multiplied by itself 0 times is always 1, the result of (22 32 42)0 is 1.
In summary, the value of (22 32 42)0 is 1.
1.8 × 1011 is equal to:- a)180000000000
- b)18000000000
- c)1800000000
- d)1800000000000
Correct answer is option 'A'. Can you explain this answer?
1.8 × 1011 is equal to:
a)
180000000000
b)
18000000000
c)
1800000000
d)
1800000000000
|
Hannah Snyder answered |
1.8 is a numerical value that falls between 1 and 2. It can represent a measurement, quantity, or any other numerical value that is slightly less than 2.
________ is the inverse operation of square.
- a)Square root
- b)Cube root
- c)Square
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
________ is the inverse operation of square.
a)
Square root
b)
Cube root
c)
Square
d)
none of these
|
|
Rajeev Kumar answered |
The inverse of squaring a number is square root.
The value of (34)3 is:- a)3
- b)312
- c)37
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
The value of (34)3 is:
a)
3
b)
312
c)
37
d)
None of the above
|
|
Hannah Cooper answered |
Explanation:
To solve this problem, we need to understand the concept of exponentiation.
Exponentiation:
Exponentiation is the mathematical operation of raising a number to a power. In simple terms, it means multiplying a number by itself multiple times.
The expression (34)3 can be read as "34 raised to the power of 3" or "34 cubed."
Calculating (34)3:
To calculate (34)3, we need to multiply 34 by itself three times.
34 * 34 * 34 = 1156 * 34 = 39304
Therefore, the value of (34)3 is 39304.
Answer:
The correct answer is option B) 312.
To solve this problem, we need to understand the concept of exponentiation.
Exponentiation:
Exponentiation is the mathematical operation of raising a number to a power. In simple terms, it means multiplying a number by itself multiple times.
The expression (34)3 can be read as "34 raised to the power of 3" or "34 cubed."
Calculating (34)3:
To calculate (34)3, we need to multiply 34 by itself three times.
34 * 34 * 34 = 1156 * 34 = 39304
Therefore, the value of (34)3 is 39304.
Answer:
The correct answer is option B) 312.
What will be the number of zeros in the square of 400?- a)4
- b)1
- c)3
- d)2
Correct answer is option 'A'. Can you explain this answer?
What will be the number of zeros in the square of 400?
a)
4
b)
1
c)
3
d)
2
|
|
Rajeev Kumar answered |
Square of 400 = 160000
Hence, the number of zeroes is 4
What is the result when 5,678,732 is rounded to the nearest thousand and then put in scientific notation? - a)5.679 × 10−6
- b)5.678 × 106
- c)5.679 × 103
- d)5.679 × 106
Correct answer is option 'D'. Can you explain this answer?
What is the result when 5,678,732 is rounded to the nearest thousand and then put in scientific notation?
a)
5.679 × 10−6
b)
5.678 × 106
c)
5.679 × 103
d)
5.679 × 106
|
Thomas Montgomery answered |
Rounding to the Nearest Thousand:
To round 5,678,732 to the nearest thousand, we look at the hundreds place, which is 8. Since 8 is greater than or equal to 5, we round up the thousands place. Therefore, 5,678,732 rounded to the nearest thousand is 5,679,000.
Expressing in Scientific Notation:
In scientific notation, we represent a number as the product of a number between 1 and 10 and a power of 10. To convert 5,679,000 to scientific notation, we move the decimal point to the left until we have a number between 1 and 10. We move the decimal point 6 places to the left to get 5.679.
Since we moved the decimal point 6 places to the left, we need to multiply by 10^6 to account for this shift.
Therefore, 5,679,000 in scientific notation is 5.679 x 10^6.
Therefore, when 5,678,732 is rounded to the nearest thousand and then put in scientific notation, the result is 5.679 x 10^6.
Convert from decimal to scientific notation:0.0000034- a)3.4 × 10−5
- b)3.4 × 106
- c)3.4 × 10−4
- d)3.4 × 10−6
Correct answer is option 'D'. Can you explain this answer?
Convert from decimal to scientific notation:
0.0000034
a)
3.4 × 10−5
b)
3.4 × 106
c)
3.4 × 10−4
d)
3.4 × 10−6
|
|
Orion Classes answered |
In this case you have to move the decimal point 6 places to the right. When you move the decimal point to the right the exponent becomes negative. Similarly when you move the decimal point to the left the exponent is positive. Also, to the left of the decimal place there can be only one digit.
3.4∗10−6
3-2 x 3-5 is equal to:- a)3-7
- b)3-3
- c)3-10
- d)37
Correct answer is option 'A'. Can you explain this answer?
3-2 x 3-5 is equal to:
a)
3-7
b)
3-3
c)
3-10
d)
37
|
|
Orion Classes answered |
3-2 x 3-5 = (1/32) x (1/35)
= (1/32+5)
= (1/37)
= 3-7
If (–3)m+1 × (–3)5 = (–3)7, then the value of m is:- a)5
- b)7
- c)1
- d)3
Correct answer is option 'C'. Can you explain this answer?
If (–3)m+1 × (–3)5 = (–3)7, then the value of m is:
a)
5
b)
7
c)
1
d)
3
|
|
Orion Classes answered |
(–3)m+1 × (–3)5 = (–3)7
(-3)m+1+5 = (-3)7
(-3)m+6 = (-3)7
54/52 is equal to:- a)56
- b)5-6
- c)5-2
- d)52
Correct answer is option 'D'. Can you explain this answer?
54/52 is equal to:
a)
56
b)
5-6
c)
5-2
d)
52
|
|
Ayesha Joshi answered |
By exponent law:
am/an = am-n
54/52 = 54-2 = 52
700000000 is equal to:- a)7 × 108
- b)7 × 107
- c)7 × 106
- d)7 × 109
Correct answer is option 'A'. Can you explain this answer?
700000000 is equal to:
a)
7 × 108
b)
7 × 107
c)
7 × 106
d)
7 × 109
|
Victoria Walsh answered |
Explanation:
Conversion:
- To convert 700,000,000 into scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point.
- This means moving the decimal point 8 places to the left, which gives us 7.0 x 10^8.
- Therefore, 700,000,000 is equal to 7 x 10^8.
Therefore, the correct answer is option A) 7 x 10^8.
Find the square root of 729.- a)29
- b)28
- c)27
- d)30
Correct answer is option 'C'. Can you explain this answer?
Find the square root of 729.
a)
29
b)
28
c)
27
d)
30
|
|
Aarav Sharma answered |
The square root of 729 is 27.
What is the least number to be added to 4523 to make it a perfect square?- a)101
- b)105
- c)110
- d)238
Correct answer is option 'A'. Can you explain this answer?
What is the least number to be added to 4523 to make it a perfect square?
a)
101
b)
105
c)
110
d)
238
|
|
Pankaj Mehra answered |
Calculation of the Perfect Square:
To find the least number that needs to be added to 4523 to make it a perfect square, we can start by determining the nearest perfect square to 4523.
The square root of 4523 is approximately 67.26. Therefore, the nearest perfect square is 67^2 (4489).
Finding the Difference:
To determine the difference between the nearest perfect square and 4523, we subtract 4489 from 4523:
4523 - 4489 = 34
Finding the Next Perfect Square:
Since the difference is positive, we need to find the next perfect square after 4523. We add twice the square root of 4523 (i.e., 2 * 67.26 ≈ 134.52) plus one to 4523:
4523 + 134.52 + 1 ≈ 4660.52
The square root of 4660.52 is approximately 68.25. Therefore, the next perfect square is 68^2 (4624).
Calculating the Least Number to be Added:
To find the least number to be added to 4523, we subtract 4523 from 4624:
4624 - 4523 = 101
Therefore, the least number that needs to be added to 4523 to make it a perfect square is 101.
Conclusion:
Based on the calculations, the correct answer is option 'A', which is 101.
To find the least number that needs to be added to 4523 to make it a perfect square, we can start by determining the nearest perfect square to 4523.
The square root of 4523 is approximately 67.26. Therefore, the nearest perfect square is 67^2 (4489).
Finding the Difference:
To determine the difference between the nearest perfect square and 4523, we subtract 4489 from 4523:
4523 - 4489 = 34
Finding the Next Perfect Square:
Since the difference is positive, we need to find the next perfect square after 4523. We add twice the square root of 4523 (i.e., 2 * 67.26 ≈ 134.52) plus one to 4523:
4523 + 134.52 + 1 ≈ 4660.52
The square root of 4660.52 is approximately 68.25. Therefore, the next perfect square is 68^2 (4624).
Calculating the Least Number to be Added:
To find the least number to be added to 4523, we subtract 4523 from 4624:
4624 - 4523 = 101
Therefore, the least number that needs to be added to 4523 to make it a perfect square is 101.
Conclusion:
Based on the calculations, the correct answer is option 'A', which is 101.
The multiplicative inverse of 7-2 is:- a)72
- b)7
- c)1/72
- d)1/7
Correct answer is option 'A'. Can you explain this answer?
The multiplicative inverse of 7-2 is:
a)
72
b)
7
c)
1/72
d)
1/7
|
|
Scarlett Coleman answered |
The multiplicative inverse of a number is the reciprocal of that number. In other words, if we multiply a number by its multiplicative inverse, the result is always 1.
To find the multiplicative inverse of 7-2, we need to find the reciprocal of 7-2.
Let's calculate it step by step:
Step 1: Find the reciprocal of 7-2
The reciprocal of a number is obtained by flipping the numerator and denominator. In this case, the numerator is 1 and the denominator is 7-2.
Reciprocal of 7-2 = (7-2)/1 = 1/(7-2)
Step 2: Simplify the expression
To simplify the expression, we need to evaluate 7-2.
7-2 = 5
So, the reciprocal of 7-2 is 1/5.
Therefore, the multiplicative inverse of 7-2 is 1/5.
Now, let's analyze the options given:
a) 72
This option is incorrect as it does not represent the reciprocal of 7-2.
b) 7
This option is incorrect as it does not represent the reciprocal of 7-2.
c) 1/72
This option is incorrect as it does not represent the reciprocal of 7-2.
d) 1/7
This option is incorrect as it does not represent the reciprocal of 7-2.
Therefore, the correct answer is option 'A' - 1/5.
To find the multiplicative inverse of 7-2, we need to find the reciprocal of 7-2.
Let's calculate it step by step:
Step 1: Find the reciprocal of 7-2
The reciprocal of a number is obtained by flipping the numerator and denominator. In this case, the numerator is 1 and the denominator is 7-2.
Reciprocal of 7-2 = (7-2)/1 = 1/(7-2)
Step 2: Simplify the expression
To simplify the expression, we need to evaluate 7-2.
7-2 = 5
So, the reciprocal of 7-2 is 1/5.
Therefore, the multiplicative inverse of 7-2 is 1/5.
Now, let's analyze the options given:
a) 72
This option is incorrect as it does not represent the reciprocal of 7-2.
b) 7
This option is incorrect as it does not represent the reciprocal of 7-2.
c) 1/72
This option is incorrect as it does not represent the reciprocal of 7-2.
d) 1/7
This option is incorrect as it does not represent the reciprocal of 7-2.
Therefore, the correct answer is option 'A' - 1/5.
Find the multiplicative inverse of 5-3.- a)53
- b)⅕
- c)52
- d)5-2
Correct answer is option 'A'. Can you explain this answer?
Find the multiplicative inverse of 5-3.
a)
53
b)
⅕
c)
52
d)
5-2
|
|
Chirag raman answered |
Explanation:
Finding the Multiplicative Inverse:
To find the multiplicative inverse of a number, we need to find a number that, when multiplied by the given number, gives a product of 1. In mathematical terms, the multiplicative inverse of a number 'a' is 1/a.
Given Number:
The given number is 5-3.
Calculating the Multiplicative Inverse:
To find the multiplicative inverse of 5-3, we need to calculate 1/(5-3).
1/(5-3) = 1/2 = 0.5
Therefore, the multiplicative inverse of 5-3 is 0.5, which is equivalent to 1/(5-3).
Final Answer:
The correct multiplicative inverse of 5-3 is 0.5, which is represented as option 'A' in the given choices.
Chapter doubts & questions for Squaring, Exponents and Square Roots - Mathematics for ACT 2025 is part of ACT exam preparation. The chapters have been prepared according to the ACT exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for ACT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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