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All questions of Square Roots and Cube Roots for UPSC CSE Exam
36 x K is a perfect cube number, then K = ______a)6b)5c)4d)3Correct answer is option 'A'. Can you explain this answer?
|
Kavya Saxena answered |
6×6=36 and 36×6=216, which is the cube of 6.
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.
Ones place digit in the cube of 5832 is ______.- a)5
- b)7
- c)2
- d)8
Correct answer is option 'D'. Can you explain this answer?
Ones place digit in the cube of 5832 is ______.
a)
5
b)
7
c)
2
d)
8
|
Geetika Shah answered |
A number ending with 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 0 then it's cube ends with 1 , 8 , 7 , 4 , 5 , 6 , 3 , 2 , 0 respectively
⇒ One's digit of 5832= 2
⇒ Cube of 2=23 = 8
⇒ Cube of 2=23 = 8
So, the one's digit of cube of 5832=8
A natural number is said to be a perfect cube, if it is the cube of some ________.- a)cube number
- b)square numbers
- c)natural number
- d)none of these
Correct answer is 'C'. Can you explain this answer?
A natural number is said to be a perfect cube, if it is the cube of some ________.
a)
cube number
b)
square numbers
c)
natural number
d)
none of these
|
|
Kavya Saxena answered |
A natural number is said to be a perfect cube if it is the cube of some natural number.
Example
8 = 2 x 2 x 2
8 = 2 3
8 is the perfect cube because it is a cube of 2 which is a natural number.
But 12 is not a perfect cube because it is not a cube of any natural numbers.
Example
8 = 2 x 2 x 2
8 = 2 3
8 is the perfect cube because it is a cube of 2 which is a natural number.
But 12 is not a perfect cube because it is not a cube of any natural numbers.
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
is :
Find the prime factorisation of 175616.- a)23×33×33×73
- b)23×23×23×73
- c)23×23×33×73
- d)23×33×53×73
Correct answer is option 'B'. Can you explain this answer?
Find the prime factorisation of 175616.
a)
23×33×33×73
b)
23×23×23×73
c)
23×23×33×73
d)
23×33×53×73
|
Ashwin Jain answered |
Prime factor tree of 175616:
So, its prime factorisation is: 2^3 x 2^3 x 2^3 x 7^3.
- a)21
- b)14
- c)12
- d)16
Correct answer is option 'D'. Can you explain this answer?
a)
21
b)
14
c)
12
d)
16
|
|
Krishna Iyer answered |
= [√248+√64]
= √248+8
= √256
= 16
= √248+8
= √256
= 16
is:
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'D'. Can you explain this answer?
a)
3
b)
4
c)
5
d)
6
|
|
Alok Verma answered |
√41-√21+√19-√9
= √41-√21+√19-3
=√41-√21+√16
=√41-√21+4
=√41-√25
=√41-5
=√36
=6
= √41-√21+√19-3
=√41-√21+√16
=√41-√21+4
=√41-√25
=√41-5
=√36
=6
What is the cube of double of ‘a’?- a)16a3
- b)2a
- c)8a3
- d)4a2
Correct answer is option 'C'. Can you explain this answer?
What is the cube of double of ‘a’?
a)
16a3
b)
2a
c)
8a3
d)
4a2
|
Vivek Rana answered |
Double of a here a+a=2a
So cube of (2a)³=8a³
- a)1
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
a)
1
b)
c)
d)
|
|
Alok Verma answered |
Cube root of (512)/125
= 8/5
Convert it into mixed fraction, we get
= 1 3/5
= 8/5
Convert it into mixed fraction, we get
= 1 3/5
What is the least perfect square which is divisible by each of 21, 36 and 66?- a)213444
- b)214434
- c)214344
- d)231444
Correct answer is option 'A'. Can you explain this answer?
What is the least perfect square which is divisible by each of 21, 36 and 66?
a)
213444
b)
214434
c)
214344
d)
231444
|
|
Alok Verma answered |
LCM of 21, 36, 66 = 2772
i.e., all multiples of 2772 are divisible by 21, 36 and 66
Prime factorization of 2772 is,
2772 = 2 × 2 × 3 × 3 × 7 × 11
i.e., to make it a perfect square, we have to multiply it by 7 and 11
Hence, required number = 2772 × 7 × 11 = 213444
i.e., all multiples of 2772 are divisible by 21, 36 and 66
Prime factorization of 2772 is,
2772 = 2 × 2 × 3 × 3 × 7 × 11
i.e., to make it a perfect square, we have to multiply it by 7 and 11
Hence, required number = 2772 × 7 × 11 = 213444
What is smallest number with which 5400 may be multiplied so that the product is perfect cube? - a) 5
- b) 3
- c) 4
- d) 6
Correct answer is option 'A'. Can you explain this answer?
What is smallest number with which 5400 may be multiplied so that the product is perfect cube?
a)
5
b)
3
c)
4
d)
6
|
Devanshi Ahuja answered |
Find prime factors of 5400
5400=2×3×3×3×2×2×5×5
If we group them in the group of 3
5400=(2×2×2)×(3×3×3)×5×5
Here to make group of 3 for 5
We have to multiply 5400 by 5.
The cube of an even number is always ____________.- a)odd number
- b)even number
- c)prime number
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The cube of an even number is always ____________.
a)
odd number
b)
even number
c)
prime number
d)
none of these
|
Biswa Ranjan Parida Pari answered |
Because multiplication of even number is always even.
for ex 2³=2.2.2=8
for ex 2³=2.2.2=8
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.
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
a)
b)
c)
d)
|
Manju Gurung answered |
√1 9/16 = √25/16 = 5/4 = 1 1/4.
Can you explain the answer of this question below:
- A:
0.1
- B:
10
- C:
10000
- D:
1000
The answer is C.
0.1
10
10000
1000
|
Thamarai Kannan answered |
10000*0.000256=2.56 √2.56 =1.6
By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?- a)2
- b)14
- c)7
- d)49
Correct answer is option 'C'. Can you explain this answer?
By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?
a)
2
b)
14
c)
7
d)
49
|
|
Amita Verma answered |
392 = 2 X 196
= 2 X 2 X 98
= 2 X 2 X 2 X 49
= 2 X 2 X 2 X 7 X 7
Thus 392 is not a perfect cube.
To make it a perfect cube multiply 392 with 7.
The least perfect square, which is divisible by each of 21, 36 and 66 is:- a)213444
- b)214344
- c)214434
- d)231444
Correct answer is option 'A'. Can you explain this answer?
The least perfect square, which is divisible by each of 21, 36 and 66 is:
a)
213444
b)
214344
c)
214434
d)
231444
|
Ishani Rane answered |
L.C.M of 21,36,66=2772
Now, 2772=2*2*3*3*7*11
Hence to make it a perfect square , it must be multiplied by 7*11
∴ The required number is 2^2*3^3*7^2*11^2
= 213444
- a)8
- b)9
- c)10
- d)12
Correct answer is option 'D'. Can you explain this answer?
a)
8
b)
9
c)
10
d)
12
|
|
Avinash Sharma answered |
As we know that (a²-b²) = (a+b) (a-b)
Therefore 14² - 2²x13 = 144.
So √144 = 12.
Therefore 14² - 2²x13 = 144.
So √144 = 12.
Express 63 as the sum of odd numbers.- a)31 + 33 + 35 + 37 + 39 + 41 + 43
- b)31 + 33 + 35 + 37 + 39 + 41
- c)31 + 33 + 35 + 37 + 39 + 41 + 43 + 45
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Express 63 as the sum of odd numbers.
a)
31 + 33 + 35 + 37 + 39 + 41 + 43
b)
31 + 33 + 35 + 37 + 39 + 41
c)
31 + 33 + 35 + 37 + 39 + 41 + 43 + 45
d)
none of these
|
Pooja Shah answered |
We know,
⇒ 31 + 33 + 35 + 37 + 39 + 41 = 216
And the cube of 6 is also 216
⇒ 6 × 6 × 6 = 216
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.
- a)None of these
- b)10
- c)1
- d)0.1
Correct answer is option 'C'. Can you explain this answer?
a)
None of these
b)
10
c)
1
d)
0.1
|
|
Unnati Dubey answered |
√0.0576=√ 0.24*0.24 = 0.24*1= 0.24
so the option C is correct (*= into)
so the option C is correct (*= into)
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
Which of the following is a perfect cube ?- a)125
- b)135
- c)145
- d)115
Correct answer is option 'A'. Can you explain this answer?
Which of the following is a perfect cube ?
a)
125
b)
135
c)
145
d)
115
|
|
Athul Sen answered |
Identifying a Perfect Cube
A perfect cube is a number that can be expressed as the product of three identical factors. For example, 27 is a perfect cube because it can be expressed as 3 x 3 x 3. To determine whether a number is a perfect cube, we need to find the cube root of that number. Here, we are given four options, and we can use the cube root method to identify the perfect cube.
Solution
a) 125
The cube root of 125 is 5. Since 125 can be expressed as 5 x 5 x 5, it is a perfect cube. Therefore, option A is the correct answer.
b) 135
The cube root of 135 is approximately 5.5. Since 5.5 is not a whole number, 135 is not a perfect cube.
c) 145
The cube root of 145 is approximately 5.7. Since 5.7 is not a whole number, 145 is not a perfect cube.
d) 115
The cube root of 115 is approximately 4.8. Since 4.8 is not a whole number, 115 is not a perfect cube.
Therefore, the only perfect cube among the given options is 125, which is option A.
A perfect cube is a number that can be expressed as the product of three identical factors. For example, 27 is a perfect cube because it can be expressed as 3 x 3 x 3. To determine whether a number is a perfect cube, we need to find the cube root of that number. Here, we are given four options, and we can use the cube root method to identify the perfect cube.
Solution
a) 125
The cube root of 125 is 5. Since 125 can be expressed as 5 x 5 x 5, it is a perfect cube. Therefore, option A is the correct answer.
b) 135
The cube root of 135 is approximately 5.5. Since 5.5 is not a whole number, 135 is not a perfect cube.
c) 145
The cube root of 145 is approximately 5.7. Since 5.7 is not a whole number, 145 is not a perfect cube.
d) 115
The cube root of 115 is approximately 4.8. Since 4.8 is not a whole number, 115 is not a perfect cube.
Therefore, the only perfect cube among the given options is 125, which is option A.
What will be the unit digit of the cube of a number ending with 6 ?
- a)4
- b)6
- c)2
- d)8
Correct answer is option 'B'. Can you explain this answer?
What will be the unit digit of the cube of a number ending with 6 ?
a)
4
b)
6
c)
2
d)
8
|
|
Kavya Datta answered |
The unit digit of a number ending with 6 will always be 6 itself when it is cubed. This can be explained using the concept of cyclicity of numbers.
Cyclicity refers to the pattern in which the unit digit of a number repeats itself when the number is raised to different powers. For example, if we consider the unit digits of the numbers 6, 6^2, 6^3, 6^4, and so on, we can observe the following pattern:
6^1 = 6
6^2 = 36
6^3 = 216
6^4 = 1296
6^5 = 7776
6^6 = 46656
From the above pattern, we can see that the unit digit of 6^1, 6^2, 6^3, and so on is always 6. Therefore, when a number ending with 6 is cubed, the unit digit will also be 6.
To further understand this concept, we can also use the concept of remainders when dividing numbers by 10. When a number is divided by 10, the remainder gives us the unit digit of the number. For example, when we divide 16 by 10, the remainder is 6.
Now, let's consider the cube of 16. When we calculate 16^3, we can write it as (10 + 6)^3. Expanding this expression using the binomial theorem, we get:
16^3 = (10 + 6)^3 = 10^3 + 3 * 10^2 * 6 + 3 * 10 * 6^2 + 6^3
The first three terms in the expansion, 10^3, 3 * 10^2 * 6, and 3 * 10 * 6^2, will all have 0 as their unit digit because they are multiples of 10. The last term, 6^3, will have a unit digit of 6.
Therefore, the unit digit of the cube of a number ending with 6 will always be 6. Hence, the correct answer is option 'B'.
Cyclicity refers to the pattern in which the unit digit of a number repeats itself when the number is raised to different powers. For example, if we consider the unit digits of the numbers 6, 6^2, 6^3, 6^4, and so on, we can observe the following pattern:
6^1 = 6
6^2 = 36
6^3 = 216
6^4 = 1296
6^5 = 7776
6^6 = 46656
From the above pattern, we can see that the unit digit of 6^1, 6^2, 6^3, and so on is always 6. Therefore, when a number ending with 6 is cubed, the unit digit will also be 6.
To further understand this concept, we can also use the concept of remainders when dividing numbers by 10. When a number is divided by 10, the remainder gives us the unit digit of the number. For example, when we divide 16 by 10, the remainder is 6.
Now, let's consider the cube of 16. When we calculate 16^3, we can write it as (10 + 6)^3. Expanding this expression using the binomial theorem, we get:
16^3 = (10 + 6)^3 = 10^3 + 3 * 10^2 * 6 + 3 * 10 * 6^2 + 6^3
The first three terms in the expansion, 10^3, 3 * 10^2 * 6, and 3 * 10 * 6^2, will all have 0 as their unit digit because they are multiples of 10. The last term, 6^3, will have a unit digit of 6.
Therefore, the unit digit of the cube of a number ending with 6 will always be 6. Hence, the correct answer is option 'B'.
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Square Root and Cube Root" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations. Q. The cube root of .000216 is:- a)0.6
- b)0.06
- c)77
- d)87
Correct answer is option 'B'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Square Root and Cube Root" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
Q. The cube root of .000216 is:
a)
0.6
b)
0.06
c)
77
d)
87
|
|
Ishani Rane answered |
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