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.
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 knowing that table well is the quickest 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. Children in England learn to recognise them in Year 5, and use them all through the 11+.
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. At primary school, "the square root" means the positive one, 11. Multiplying negative numbers comes later, at secondary school.
Number facts are the base of 11+ maths
Factors, multiples, primes and square numbers come up all over 11+ maths, from simplifying fractions to ratio. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.