How to Find the Square Root of a Perfect Square

How to Find the Square Root of a Perfect Square

A perfect square is a number that is the square of an integer. Its square root is always a whole number.

Method 1 — Memorisation

Know the squares from 1² to 15²: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. These cover most questions you will encounter.

Method 2 — Prime factorisation

Factorise the number into primes, pair them up, take one from each pair. Example: √144 = √(2×2×2×2×3×3) = 2×2×3 = 12.

Method 3 — Repeated subtraction

Subtract consecutive odd numbers (1,3,5,7…) from the number. Count how many subtractions until you reach 0. That count is the square root. Example: 16 − 1=15, 15−3=12, 12−5=7, 7−7=0. 4 subtractions → √16 = 4.

List of perfect squares 1–400

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400