Basics of Square Roots

Because squaring any real number gives a non-negative result, no real number multiplied by itself ever produces a negative answer. This means the square root of a negative number does not exist within real numbers, so expressions like the square root of minus one have no real value.

Although minus 3 squared also equals 9, the square root is defined as the non-negative answer. By definition, the radical sign always returns the non-negative root. Whenever you see the tick-like sign, associate it with a non-negative number, so the square root of 9 is 3, not minus 3.

The square root of 0 is 0, because 0 multiplied by itself gives 0. Zero counts as non-negative, so it satisfies the definition of a square root. Zero is also the only number whose square root is itself, since squaring any other number gives a different value.

Knowing the perfect squares from 1 squared up to 15 squared turns most GCSE square root questions into instant recall. When you recognise 144 as 12 squared or 196 as 14 squared, you save time, avoid calculator errors, and keep your work fluent in non-calculator tests.

The radical sign, which looks like a tick (√), tells you to find the non-negative square root of the number underneath it. Whenever you spot this symbol, associate it with a non-negative answer, never a negative one. It marks the squaring operation carried out in reverse.