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.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
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.
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. This list starts with the positive square numbers. Zero is also a square number: 0 × 0 = 0.
Can a square root be negative?
Yes. −1 × −1 also makes 1, so −1 is a square root of 1 too. For a positive number, the symbol √ denotes the positive root, 1. The negative root also gives 1 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.