Quantitative Aptitude · Mathematics

Squares and Square Roots

191 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 and square root perfect square or square number squares and triangles powers and roots

Is $2352$ a perfect square ? If not, find the greater number closest to $2352$,  which is a perfect square. Find the square root of the new number.

  1. <span class="block ng-binding">Yes, $2352$ a perfect square.
  2. No, $2352$ is not a perfect square else $2304$ is closest perfect square.
    Square root of $2304\ is\ 48$
  3. No, $2352$ is not a perfect square else $2401$ is closest perfect square.
    Square root of $2401\ is\ 49$

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We have 2352 =  $ \displaystyle \underline{2\times 2}\times \underline{2\times 2}\times 3\times \underline{7\times 7} $
As the prime factor 3 has no pair 2352 is not a perfect square 

Nearest no. bigger than  $2352$ and square is $2401 =49\times49$

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

$025$ is square of $55$.What digit should replace $$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Step 1: 

Multiply ten's digit with its next number.
$5 \times (5 + 1) = 5 \times 6 = 30 ---(1)$
Step 2:Find the square of unit's digit: 5
$5^2$ = 25 ----(2)
Step 3 :
Joining (1) and (2), we get
$3025 = 55 \times 55$
So, 3 is the missing number.

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

If a four-digit perfect square number is such that the number formed by the first two digits and the number formed by the last two digits are also perfect squares, identify the four digit number.

  1. $6416$
  2. $3616$
  3. $1681$
  4. $1664$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Four digit number $accd$

$ab$ is a perfect square
$cd$ is also a perfect square
Consider $6416$
$64$and$16$ are perfect square but $6416$ is not a perfect square.
Consider $3616$
$36$and$16$ are perfect square but $3616$ is not a perfect square.

Consider $1681$
$16$and$81$ are perfect square and $1681$ is a perfect square.

Consider $1664$
$16$and$64$ are perfect square but $1664$ is not a perfect square.
Hence, Option C is correct.


Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

Divide $16$ into two parts such that the twice of the square of the greater part exceeds the square of the smaller part by $164.$

  1. $6, 10$
  2. $6, 4$
  3. $4, 10$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the larger part be $x$

So, smaller part is $16-x$
Given, 
$2\times x^2 = \left(16-x\right)^2 + 164$
$2x^2 = \left(256-32x+x^2\right) +164$
$x^2 +32x -420 = 0$
$x^2 -10x +42x - 420 =0$
$ x \left(x-10 \right) +42 \left(x - 10 \right) = 0$
$\left(x - 10 \right) \left(x+42\right)$
$\rightarrow x = 10, -42$
$\because \ x$ cannot be negative, hence $x = 10$
So, the two parts are $10, 6$

Multiple choice

Which of these is a square number?

  1. 3

  2. 28

  3. 25

  4. 33
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A square number is the result of multiplying an integer by itself. Since 5 multiplied by 5 equals 25, it is a square number.