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

Which is the smallest perfect number?

  1. 2

  2. 6

  3. 3

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

A perfect number is a positive integer equal to the sum of its proper divisors (excluding itself). 6 is the smallest perfect number because its proper divisors are 1, 2, 3, and 1 + 2 + 3 = 6. The next perfect number is 28 (1 + 2 + 4 + 7 + 14 = 28). 2, 3, and 4 are not perfect numbers as their proper divisors don't sum to themselves.

Multiple choice

The sum of 4 consecutive two-digit natural numbers, when divided by 10, becomes a perfect square. What is the least possible value of the largest of the four numbers?

  1. 5.5

  2. 93

  3. 13

  4. Can’t be determined

  5. 163
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the 4 consecutive odd numbers be x - 3, x - 1, x + 1 and x + 3. Sum of these numbers is 4x. √4x/10 or 2√x/10 is a perfect square. Now take different values of x. At x = 10, it becomes a perfect square. So, the four numbers are 7, 9, 11 and 13.

Multiple choice

How many squares on the Chess Board?

  1. 49

  2. 64

  3. 81

  4. 82
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A standard chess board has 8 rows and 8 columns of squares, totaling 64 squares (8 × 8 = 64). This includes the alternating light and dark colored squares that players use to move pieces according to the rules of chess.