Square root of 64
√64 = 8. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 64 is 8, because 8 × 8 = 64.
64 drawn as a square
64 counters make a perfect square: 8 rows of 8. The length of the side is the square root.
How to work out √64
A square root asks: which number, times itself, makes 64? 8 × 8 = 64, so √64 = 8. Squaring and square rooting undo each other: 8 squared is 64, and the square root of 64 is 8.
There is a pattern in the square numbers too. Add up the first 8 odd numbers and you get 64: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64. Each new odd number is the extra row and column of counters that makes the next square.
8 × 8 is in the 8 times table, so knowing that table well is the quickest way to recognise 64 as a square number.
Square numbers and their roots
The square numbers up to 144 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. Children in England learn to recognise them in Year 5, and use them all through the 11+.
More numbers
See every factor of 64 or check whether 64 is prime.
Questions parents ask
A square has an area of 64 cm². How long is each side?
8 cm, because 8 cm × 8 cm = 64 cm². Working out the side of a square from its area is finding a square root.
What is 64 squared?
64 × 64 = 4096. Squaring 64 makes a much bigger number, while its square root, 8, is smaller.
Which square numbers come either side of 64?
49 (7 × 7) before it and 81 (9 × 9) after it. They are 15 below and 17 above 64.
Can a square root be negative?
Yes. −8 × −8 also makes 64, so −8 is a square root of 64 too. At primary school, "the square root" means the positive one, 8. Multiplying negative numbers comes later, at secondary school.
Number facts are the base of 11+ maths
Factors, multiples, primes and square numbers come up all over 11+ maths, from simplifying fractions to ratio. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.