How do you simplify $sqrt(18)$ without a calculator?

Question

3490 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-02T10:16:25

One way to simplify this number is to look for alternative ways of writing the number that's under the square root sign.

You must extract the square root from $"18"$ , which isn't a perfect square. However, if you look closely at this number you'll find that

$18 = 9 * 2$

You know that $"9"$ is a perfect square, which means that

$18 = 3^(2) * 2$

Stick this under the square root and you'll get

$sqrt(18) = sqrt(3^(2) * 2) = sqrt(3^(2)) * sqrt(2) = 3sqrt(2)$

How do you simplify sqrt(18)sqrt(18) without a calculator?