Square root of 144
√144 = 12. Here is why, drawn as a square and checked with a multiplication.
The answer
The square root of 144 is 12, because 12 × 12 = 144.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
144 drawn as a square
144 counters make a perfect square: 12 rows of 12. The length of the side is the square root.
How to work out √144
A square root asks: which number, times itself, makes 144? 12 × 12 = 144, so √144 = 12. Squaring and square rooting undo each other: 12 squared is 144, and the square root of 144 is 12.
There is a pattern in the square numbers too. Add up the first 12 odd numbers and you get 144: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = 144. Each new odd number is the extra row and column of counters that makes the next square.
12 × 12 is in the 12 times table, so that table gives you a way to recognise 144 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 144 cm². How long is each side?
12 cm, because 12 cm × 12 cm = 144 cm². Working out the side of a square from its area is finding a square root.
What is 144 squared?
144 × 144 = 20736. Squaring 144 makes a much bigger number, while its square root, 12, is smaller.
Which square numbers come either side of 144?
121 (11 × 11) before it and 169 (13 × 13) after it. They are 23 below and 25 above 144.
Can a square root be negative?
Yes. −12 × −12 also makes 144, so −12 is a square root of 144 too. For a positive number, the symbol √ denotes the positive root, 12. The negative root also gives 144 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.