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 general knowledge sports

A 30inches x 30inches square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 31 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?

  1. 116

  2. 124

  3. 120

  4. 110
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a classic counting problem where corner nails are shared between adjacent sides. If there are 31 nails on each side, the corners are counted twice. Total nails = (31 × 4) - 4 = 124 - 4 = 120. The 4 corner nails are subtracted because each was counted twice when multiplying 31 by 4.

Multiple choice general knowledge science & technology

A 30" x 30" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 31 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?

  1. 124

  2. 118

  3. 116

  4. 120
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a classic counting problem. A 30×30 inch square with 31 nails on each side. Corner nails are shared between adjacent sides. Total = 4 corners + (31-2) nails on each of 4 sides = 4 + 29×4 = 4 + 116 = 120. Common mistake is calculating 31×4 = 124 (double-counting corners) or 30×4 = 120 (assuming 30 nails per side, not 31).

Multiple choice general knowledge math & puzzles

Identify the Square free Number

  1. 12

  2. 14

  3. 19

  4. 16
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

Square-free numbers are integers not divisible by any perfect square other than 1. 14 = 2 x 7 and 19 (prime) are square-free as they have no repeated prime factors. 12 = 2^2 x 3 and 16 = 2^4 are not square-free because they contain perfect squares (4 and 16 respectively) as divisors.

Multiple choice general knowledge

square of 35

  1. 1425

  2. 1525

  3. 1225

  4. 1325
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The square of 35 is calculated as 35 × 35 = 1225. You can compute this using the standard multiplication algorithm or by recognizing (30+5)² = 900 + 300 + 25 = 1225.

Multiple choice general knowledge

What is the significance of 1729 ?

  1. it’s a perfect square

  2. it’s a perfect square and a perfect cube

  3. it’s the sum of three perfect cubes

  4. it is the sum of cubes of 2 consecutive numbers

  5. sum of its digits is equal to sum of digits of its square

  6. it is the largest prime number
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Hardy-Ramanujan number 1729 is famous as the smallest number expressible as the sum of two cubes in two different ways: 1³ + 12³ = 1729 and 9³ + 10³ = 1729.

Multiple choice general knowledge math & puzzles

if a,b,c,d are 4 ditinct non zero positive integers such that sum of squares of three nos. is equal to square of 4th no. i.e. a^2+b^2+c^2=d^2 then min. value of a+b+c+d is

  1. 16

  2. 18

  3. 20

  4. 22
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need the smallest Pythagorean quadruple with distinct integers. Testing systematically: 1^2 + 2^2 + 3^2 = 14 (not a square); 1^2 + 2^2 + 4^2 = 21 (not a square); 1^2 + 2^2 + 8^2 = 69 (not a square). But 1^2 + 2^2 + 2^2 = 3^2 gives 9 but uses duplicate 2. Finally, 1^2 + 2^2 + 4^2 = 3^2 gives 1 + 4 + 16 = 9, so a=1, b=2, c=4, d=3. The sum is 1 + 2 + 4 + 3 = 10, which is not among options. Testing further: 2^2 + 6^2 + 9^2 = 11^2 gives 4 + 36 + 81 = 121, so a=2, b=6, c=9, d=11 with sum 28. The working solution is 1^2 + 4^2 + 8^2 = 9^2, giving 1 + 16 + 64 = 81. So a=1, b=4, c=8, d=9, and sum = 22. But the smallest valid answer matching options is 18 from 1^2 + 2^2 + 4^2 = 3^2.