Square root of 121
√121 = 11. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 121 is 11, because 11 × 11 = 121.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
121 drawn as a square
121 counters make a perfect square: 11 rows of 11. The length of the side is the square root.
How to work out √121
A square root asks: which number, times itself, makes 121? 11 × 11 = 121, so √121 = 11. Squaring and square rooting undo each other: 11 squared is 121, and the square root of 121 is 11.
There is a pattern in the square numbers too. Add up the first 11 odd numbers and you get 121: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 121. Each new odd number is the extra row and column of counters that makes the next square.
11 × 11 is in the 11 times table, so that table gives you a way to recognise 121 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
Questions parents ask
A square has an area of 121 cm². How long is each side?
11 cm, because 11 cm × 11 cm = 121 cm². Working out the side of a square from its area is finding a square root.
What is 121 squared?
121 × 121 = 14641. Squaring 121 makes a much bigger number, while its square root, 11, is smaller.
Which square numbers come either side of 121?
100 (10 × 10) before it and 144 (12 × 12) after it. They are 21 below and 23 above 121.
Can a square root be negative?
Yes. −11 × −11 also makes 121, so −11 is a square root of 121 too. For a positive number, the symbol √ denotes the positive root, 11. The negative root also gives 121 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.