Square root of 9
√9 = 3. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 9 is 3, because 3 × 3 = 9.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
9 drawn as a square
9 counters make a perfect square: 3 rows of 3. The length of the side is the square root.
How to work out √9
A square root asks: which number, times itself, makes 9? 3 × 3 = 9, so √9 = 3. Squaring and square rooting undo each other: 3 squared is 9, and the square root of 9 is 3.
There is a pattern in the square numbers too. Add up the first 3 odd numbers and you get 9: 1 + 3 + 5 = 9. Each new odd number is the extra row and column of counters that makes the next square.
3 × 3 is in the 3 times table, so that table gives you a way to recognise 9 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.
More numbers
See every factor of 9 or check whether 9 is prime.
Questions parents ask
A square has an area of 9 cm². How long is each side?
3 cm, because 3 cm × 3 cm = 9 cm². Working out the side of a square from its area is finding a square root.
What is 9 squared?
9 × 9 = 81. Squaring 9 makes a much bigger number, while its square root, 3, is smaller.
Which square numbers come either side of 9?
4 (2 × 2) before it and 16 (4 × 4) after it. They are 5 below and 7 above 9.
Can a square root be negative?
Yes. −3 × −3 also makes 9, so −3 is a square root of 9 too. For a positive number, the symbol √ denotes the positive root, 3. The negative root also gives 9 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.