How do you simplify the square root of 18 without using a calculator?

Surds can be simplified if the number in the square root has a square number as a factor. It is also worth remembering that SQRT(ab) = SQRT(a) x SQRT(b). So if you combine these two points, lets look at how we can simplify the square root of 18.

A factor of 18 that is a square number is 9. Therefore SQRT(18) = SQRT(9) x SQRT(2). The square root of 9 is 3, so we can now write our final answer as SQRT(18) = 3 x SQRT(2). To check you’ve understood this, you might like to have a go at simplifying these two surds. A) SQRT(20)  B) SQRT(32)