Square root of 1
√1 = 1. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 1 is 1, because 1 × 1 = 1.
1 drawn as a square
One counter on its own is already a square, with sides 1 long. The length of the side is the square root.
How to work out √1
A square root asks: which number, times itself, makes 1? 1 × 1 = 1, so √1 = 1. Squaring and square rooting undo each other: 1 squared is 1, and the square root of 1 is 1.
1 is the only number (apart from 0) that is its own square root, because 1 × 1 = 1.
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
Questions parents ask
A square has an area of 1 cm². How long is each side?
1 cm, because 1 cm × 1 cm = 1 cm². Working out the side of a square from its area is finding a square root.
Which square number comes after 1?
4, because 2 × 2 = 4. 1 is the first square number children meet at primary school. (Some books also count 0 = 0 × 0, but primary lists start at 1.)
Can a square root be negative?
Yes. −1 × −1 also makes 1, so −1 is a square root of 1 too. At primary school, "the square root" means the positive one, 1. 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.