Square root of 81
√81 = 9. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 81 is 9, because 9 × 9 = 81.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
81 drawn as a square
81 counters make a perfect square: 9 rows of 9. The length of the side is the square root.
How to work out √81
A square root asks: which number, times itself, makes 81? 9 × 9 = 81, so √81 = 9. Squaring and square rooting undo each other: 9 squared is 81, and the square root of 81 is 9.
There is a pattern in the square numbers too. Add up the first 9 odd numbers and you get 81: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81. Each new odd number is the extra row and column of counters that makes the next square.
9 × 9 is in the 9 times table, so that table gives you a way to recognise 81 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 81 or check whether 81 is prime.
Questions parents ask
A square has an area of 81 cm². How long is each side?
9 cm, because 9 cm × 9 cm = 81 cm². Working out the side of a square from its area is finding a square root.
What is 81 squared?
81 × 81 = 6561. Squaring 81 makes a much bigger number, while its square root, 9, is smaller.
Which square numbers come either side of 81?
64 (8 × 8) before it and 100 (10 × 10) after it. They are 17 below and 19 above 81.
Can a square root be negative?
Yes. −9 × −9 also makes 81, so −9 is a square root of 81 too. For a positive number, the symbol √ denotes the positive root, 9. The negative root also gives 81 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.