Quantitative Aptitude · Mathematics

Squares and Square Roots

196 Questions

Squares and square roots questions assess numerical ability through perfect squares, digit properties, and fast calculation techniques. Many competitive exams feature Vedic mathematics shortcuts to solve these quickly. Mastering these rules improves overall calculation speed.

Perfect square propertiesVedic math squaresFinding square rootsDigit replacement puzzlesLeast perfect squares

Squares and Square Roots Questions

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

If it is possible to form a number with the second, the fifth and the eighth digits of the number 31549786, which is the perfect square of a two digit even number, which of the following will be the second digit of that even number?

  1. 1

  2. 4

  3. 6

  4. No such number can be formed
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The 2nd , 5th and 8th digit of the number 31549786 are 196 respectively.
196 is a perfect square of 14. 
Therefore, the even number required is 14.
Second digit of that number is 4.
Answer is 4

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

For each of the following, find the least number that must be added so that the resulting number is a perfect square. 7172

  1. 23

  2. 65

  3. 15

  4. 53
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the number to add, calculate the square root of 7172, which is approximately 84.68. The next perfect square is 85^2 = 7225. The difference is 7225 - 7172 = 53.

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

The least number which must be subtracted from 6,156 to make it a perfect square is:

  1. 62

  2. 72

  3. 52

  4. 82
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
First we will find the square root of $6156$:

$\sqrt { 6156 } =\sqrt { 2×2×3×3×3×3×19 } =2×3×3×\sqrt { 19 } =18×4.358=78.444...$

Now, we find the square of $78$ as follows:

${ 78 }^{ 2 }=78×78=6084$

Let us now subtract $6156$ from $6084$ as shown below:

$6156 - 6084 = 72$

Hence, $72$ will be subtracted from $6156$ to make it a perfect square.

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

Two rows of numbers are given The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered The operations of numbers progress from left to right
Rules
I. If an odd number is followed by a two-digit even number then they are to be added.
II. If an odd number is followed by a two-digit odd number then the second number is to be subtracted from the first number
III. If an even number is followed by a number which is a perfect square of a number then the second number is to be divided by the first number
IV. If an even number is followed by a two-digit even number then the first number is to be multiplied by the second number
                    8  16  16  14
                   13  11  12  144
What is the difference between the resultant of the first set of numbers and the second set of numbers ?

  1. 106

  2. 118

  3. 210

  4. 222
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

How many squares are there on a chessboard?

  1. 64

  2. 32

  3. 48

  4. 81
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A chessboard has 64 squares, arranged in an 8x8 grid.

Multiple choice

How many squares are there on a chessboard?

  1. 64

  2. 81

  3. 100

  4. 121
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A chessboard consists of 64 squares arranged in an 8x8 grid, with alternating light and dark colors.

Multiple choice

What is the formula for finding the nth square number according to Virasena?

  1. $$S_n = n^2$$
  2. $$S_n = (n+1)^2$$
  3. $$S_n = (n-1)^2$$
  4. $$S_n = (n-2)^2$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Virasena, the formula for finding the nth square number is $$S_n = n^2$$

Multiple choice

How many squares are there on a typical Ludo board?

  1. 56

  2. 64

  3. 72

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A typical Ludo board consists of 56 squares, arranged in a square grid.

Multiple choice

Find the square of 108 using Nikhilam Sutra.

  1. 11664

  2. 12348

  3. 11764

  4. 10648
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the Nikhilam Sutra, the square of a number can be found by subtracting the sum of the digits from the number itself and then multiplying the result by the sum of the digits. In this case, 108 - (1 + 0 + 8) = 99 and 99 * (1 + 0 + 8) = 11664.

Multiple choice

Determine if 121 is a perfect square.

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A perfect square is a number that can be expressed as the square of an integer. 121 is a perfect square because it is equal to 11^2.