Square root of 100
√100 = 10. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 100 is 10, because 10 × 10 = 100.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
100 drawn as a square
100 counters make a perfect square: 10 rows of 10. The length of the side is the square root.
How to work out √100
A square root asks: which number, times itself, makes 100? 10 × 10 = 100, so √100 = 10. Squaring and square rooting undo each other: 10 squared is 100, and the square root of 100 is 10.
There is a pattern in the square numbers too. Add up the first 10 odd numbers and you get 100: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100. Each new odd number is the extra row and column of counters that makes the next square.
10 × 10 is in the 10 times table, so that table gives you a way to recognise 100 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 100 or check whether 100 is prime.
Questions parents ask
A square has an area of 100 cm². How long is each side?
10 cm, because 10 cm × 10 cm = 100 cm². Working out the side of a square from its area is finding a square root.
What is 100 squared?
100 × 100 = 10000. Squaring 100 makes a much bigger number, while its square root, 10, is smaller.
Which square numbers come either side of 100?
81 (9 × 9) before it and 121 (11 × 11) after it. They are 19 below and 21 above 100.
Can a square root be negative?
Yes. −10 × −10 also makes 100, so −10 is a square root of 100 too. For a positive number, the symbol √ denotes the positive root, 10. The negative root also gives 100 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.