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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.
The square of 23 is :- a)529
- b)526
- c)461
- d)429
Correct answer is option 'A'. Can you explain this answer?
The square of 23 is :
a)
529
b)
526
c)
461
d)
429
| | Amit Sharma answered |
Yes the correct option is A because..... 23×23=529.....
How many numbers lie between square of 12 and 13?- a)21
- b)23
- c)22
- d)24
Correct answer is option 'D'. Can you explain this answer?
How many numbers lie between square of 12 and 13?
a)
21
b)
23
c)
22
d)
24
 | Gunjan Lakhani answered |
The number of non square numbers
between n² and ( n + 1 )² is 2n
Here,
n = 12,
n + 1 = 13
Therefore ,
Number of natural numbers lie
between 12² and 13² = 2 × 12
= 24
between n² and ( n + 1 )² is 2n
Here,
n = 12,
n + 1 = 13
Therefore ,
Number of natural numbers lie
between 12² and 13² = 2 × 12
= 24
What will be the number of zeros in the square of 400 ?- a)5
- b)1
- c)3
- d)4
Correct answer is option 'D'. Can you explain this answer?
What will be the number of zeros in the square of 400 ?
a)
5
b)
1
c)
3
d)
4
 | Priyanka Sharma answered |
Square of 400 = 160000
Therefore, the number of zeroes is 4
The square root of 169 is- a)13
- b)1.3
- c)-1.3
- d)13/10
Correct answer is option 'A'. Can you explain this answer?
The square root of 169 is
a)
13
b)
1.3
c)
-1.3
d)
13/10
 | Shubham Sharma answered |
13 is the square root of 169.
The square of which of the following would be even number?- a)2826
- b)7779
- c)1057
- d)131
Correct answer is option 'A'. Can you explain this answer?
The square of which of the following would be even number?
a)
2826
b)
7779
c)
1057
d)
131
 | EduRev Class 8 answered |
Since the square of an odd natural number is odd and that of an even number is an even number.
∴ (i) The square of 431 is an odd number
(∵ 431 is an odd number)
(ii) The square of 2826 is an even nnumber.
(∵ 2826 is an even number)
(iii) The square of 7779 is an odd number
(∵ 7779 is an odd number)
(iv) The square of 131 is an odd nnumber.
(∵ 82004 is an odd number)
Which smallest number should be added to 80 so as to make it a perfect square ?- a)2
- b)3
- c)1
- d)4
Correct answer is option 'C'. Can you explain this answer?
Which smallest number should be added to 80 so as to make it a perfect square ?
a)
2
b)
3
c)
1
d)
4
 | Target Study Academy answered |
The smallest number to be added to 80 so as to obtain a perfect square number is 1.
80+1=81 and the square root of 81 is 9,so 81 becomes a perfect square.
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
 | Lakesway Classes answered |
Here, we have to find the sum of first five odd natural numbers.
Therefore, 1 + 3 + 5 + 7 + 9 = (5)2 = 25
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
 | Shiksha Academy 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
is :
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.
If (504 + p) is a perfect cube number, whose cube root is p, then p = ______.- a)6
- b)4
- c)2
- d)8
Correct answer is option 'D'. Can you explain this answer?
If (504 + p) is a perfect cube number, whose cube root is p, then p = ______.
a)
6
b)
4
c)
2
d)
8
 | BT Educators answered |
Dear Student, we know that 83= 512
So p = 512−504 = 8
So p = 512−504 = 8
Which of the following is a perfect square ?- a)45
- b)81
- c)18
- d)54
Correct answer is option 'B'. Can you explain this answer?
Which of the following is a perfect square ?
a)
45
b)
81
c)
18
d)
54
| | Pooja Shah answered |
81 is the square of 9..... 9 × 9 = 81
The perfect square number between 30 and 40 is :- a)35
- b)39
- c)36
- d)32
Correct answer is option 'C'. Can you explain this answer?
The perfect square number between 30 and 40 is :
a)
35
b)
39
c)
36
d)
32
| | Ananya Das answered |
Since 35,32,39 are not perfect squares . hence the only perfect square between 30 and 40 is 36
- 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:
Which least number should be subtracted from 629 so as to get a perfect square ?- a)4
- b)5
- c)6
- d)3
Correct answer is option 'A'. Can you explain this answer?
Which least number should be subtracted from 629 so as to get a perfect square ?
a)
4
b)
5
c)
6
d)
3
| | Preeti Khanna answered |
If we subtract 4 from the given number, then it becomes 625.
625 is a square of 25.
Hence, the answer is 4
Which is the smallest three-digit perfect square?- a)100
- b)101
- c)121
- d)144
Correct answer is option 'A'. Can you explain this answer?
Which is the smallest three-digit perfect square?
a)
100
b)
101
c)
121
d)
144
 | Shivika Kumari answered |
Yes as the the smallest 3 digit no. is 100 and it is the square of 10 so also a perfect square.
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.
Which is the greatest 4-digit perfect square?- a)9999
- b)9990
- c)9800
- d)9801
Correct answer is option 'D'. Can you explain this answer?
Which is the greatest 4-digit perfect square?
a)
9999
b)
9990
c)
9800
d)
9801
| | Ananya Das 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.
How many non square numbers lie between 112 and 122?- a)21
- b)23
- c)22
- d) 20
Correct answer is option 'C'. Can you explain this answer?
How many non square numbers lie between 112 and 122?
a)
21
b)
23
c)
22
d)
20
| | EduRev Class 8 answered |
Between 112 and 122
Here, n = 11 and n + 1 = 12
∴ Natural numbers between 112 and 122 are (2 × n) or 2 × 11, i.e. 22.
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
What could be the possible “one’s digit” of the square root of 625?- a)5
- b)0
- c)4
- d)8
Correct answer is option 'A'. Can you explain this answer?
What could be the possible “one’s digit” of the square root of 625?
a)
5
b)
0
c)
4
d)
8
| | Pooja Shah answered |
625 is square root of 25 and one's digit of 25 is 5
- a)1
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
a)
1
b)
c)
d)
 | Wizius Careers 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
Which is the smallest 4-digit perfect square?- a)1024
- b)1025
- c)1000
- d)1016
Correct answer is option 'A'. Can you explain this answer?
Which is the smallest 4-digit perfect square?
a)
1024
b)
1025
c)
1000
d)
1016
 | Sanjana Bose answered |
Greatest number of four digits = 1000.(32)^2 is more than 1000 by 24.So, the
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
- 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 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
Find the cube root of -5832.- a)-27
- b)27
- c)18
- d)-18
Correct answer is 'D'. Can you explain this answer?
Find the cube root of -5832.
a)
-27
b)
27
c)
18
d)
-18
 | Tanpreet Kaur Oberoi answered |
Multipy 18 three times u will get your answet
What will be the number of digits in the square root of 25600?- a)3
- b)2
- c)5
- d)4
Correct answer is option 'A'. Can you explain this answer?
What will be the number of digits in the square root of 25600?
a)
3
b)
2
c)
5
d)
4
| | Preeti Khanna answered |
The square root of 25600 is 160. Hence, number of digits is 3.
- 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.
By which smallest number 48 must be divided so as to make it a perfect square ?- a)2
- b)3
- c)6
- d)4
Correct answer is option 'B'. Can you explain this answer?
By which smallest number 48 must be divided so as to make it a perfect square ?
a)
2
b)
3
c)
6
d)
4
| | Anita Menon answered |
By Prime factorisation, we have 48=2*2*2*2*3. We have two pairs of 2 but no pair of 3. Hence 48 must be divided by 3 to make it a perfect square.
What will be the number of digits in the square root of 1296?- a)2
- b)3
- c)1
- d)4
Correct answer is option 'A'. Can you explain this answer?
What will be the number of digits in the square root of 1296?
a)
2
b)
3
c)
1
d)
4
| | Preeti Khanna answered |
The square root of 1296 is 36.
Hence, number of digits os 2
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.
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
The cube root of 13824 is __________.- a)36
- b)25
- c)24
- d)16
Correct answer is option 'C'. Can you explain this answer?
The cube root of 13824 is __________.
a)
36
b)
25
c)
24
d)
16
 | Anshika Locks answered |
Options 'c' because when we use division method so answer is come
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