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

What is the number of squares on a chess board?

  1. 49

  2. 81

  3. 64

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A standard chess board has 64 squares arranged in an 8x8 grid. The board consists of 32 light squares and 32 dark squares, totaling 64 squares. The 8x8 grid format has been the standard for chess since the 15th century. Options 49 (7x7), 81 (9x9), and 36 (6x6) are all incorrect grid sizes for standard chess.

Multiple choice general knowledge math & puzzles

A square is divided into 9 identical smaller squares. Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball (one ball in one square only). In how many different ways can this be done?

  1. 81

  2. 91

  3. 41

  4. 51
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a stars and bars combinatorics problem. Distributing 6 identical balls into 9 squares with each of 3 rows getting at least 1 ball means we need to count distributions where balls appear in all 3 rows. The calculation yields 81 valid arrangements.

Multiple choice general knowledge math & puzzles

A 34" x 34" 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 35 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. 136

  2. 133

  3. 132

  4. 130
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To count total nails on a square with 35 on each side, we must avoid double-counting corners. Each corner nail belongs to two sides, so total = 4 × 35 - 4 = 136. Simply multiplying 4 × 35 = 140 would count each corner twice.

Multiple choice technology

How many multiplications do you need to perform if you use Repeated Squaring technique to calculate n^1000. (Ignore the problem of storing such a large number in variable assume you can store infinitly large number in basic data types)

  1. 99

  2. 119

  3. 6

  4. 14
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Repeated squaring (exponentiation by squaring) computes n^1000 by decomposing the exponent into binary. 1000 in binary is 1111101000 (base-2), which has 10 bits requiring 9 squarings, and Hamming weight of 6 ones requiring 5 extra multiplications. Total: 9 + 5 = 14 multiplications. This is dramatically fewer than 1000 for naive multiplication.