Question

Express the following surd in simplest form.

`sqrt(162)`

Answer 1

A surd is said to be in its simplest form when the number under the root sign has no square factors.

Given,

`sqrt(162)`

Prime factors of 162 is 2 × 3 × 3 × 3 × 3

So, `sqrt(2 xx 3 xx 3 xx 3 xx 3)`

= `3 xx 3sqrt(2)`

= `9sqrt(2)`

Thus, the simplest form of `sqrt(162)` is `9sqrt(2)`.