All questions of Square Roots and Cube Roots for UPSC CSE Exam

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?

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?

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?

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.

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?

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

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?

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?

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?

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?

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 
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?

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.

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?

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?

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?

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 11and 122?
  • a)
    21
  • b)
    23
  • c)
    22
  • d)
     20
Correct answer is option 'C'. Can you explain this answer?

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.

  • a)
    1
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Wizius Careers answered
Cube root of (512)/125
= 8/5
Convert it into mixed fraction, we get
= 1 3/5

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?

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?

Alok Verma answered
√41-√21+√19-√9
= √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?

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

  • a)
    8
  • b)
    9
  • c)
    10
  • d)
    12
Correct answer is option 'D'. Can you explain this answer?

Avinash Sharma answered
As we know that  (a²-b²) = (a+b) (a-b)
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?

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.

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?

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?

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

Chapter doubts & questions for Square Roots and Cube Roots - UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making 2026 is part of UPSC CSE exam preparation. The chapters have been prepared according to the UPSC CSE exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UPSC CSE 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Chapter doubts & questions of Square Roots and Cube Roots - UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making in English & Hindi are available as part of UPSC CSE exam. Download more important topics, notes, lectures and mock test series for UPSC CSE Exam by signing up for free.

Top Courses UPSC CSE

Related UPSC CSE Content