Square root of 36
√36 = 6. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 36 is 6, because 6 × 6 = 36.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
36 drawn as a square
36 counters make a perfect square: 6 rows of 6. The length of the side is the square root.
How to work out √36
A square root asks: which number, times itself, makes 36? 6 × 6 = 36, so √36 = 6. Squaring and square rooting undo each other: 6 squared is 36, and the square root of 36 is 6.
There is a pattern in the square numbers too. Add up the first 6 odd numbers and you get 36: 1 + 3 + 5 + 7 + 9 + 11 = 36. Each new odd number is the extra row and column of counters that makes the next square.
6 × 6 is in the 6 times table, so that table gives you a way to recognise 36 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 36 or check whether 36 is prime.
Questions parents ask
A square has an area of 36 cm². How long is each side?
6 cm, because 6 cm × 6 cm = 36 cm². Working out the side of a square from its area is finding a square root.
What is 36 squared?
36 × 36 = 1296. Squaring 36 makes a much bigger number, while its square root, 6, is smaller.
Which square numbers come either side of 36?
25 (5 × 5) before it and 49 (7 × 7) after it. They are 11 below and 13 above 36.
Can a square root be negative?
Yes. −6 × −6 also makes 36, so −6 is a square root of 36 too. For a positive number, the symbol √ denotes the positive root, 6. The negative root also gives 36 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.