Question

Express the following surd in simplest form.

`sqrt(112)`

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(112)`

Prime factors of 112 is 2 × 2 × 2 × 2 × 7

So, `sqrt(2 xx 2 xx 2 xx 2 xx 7)`

= `2 xx 2sqrt(7)`

= `4sqrt(7)`

Thus, the simplest form of `sqrt(112)` is `4sqrt(7)`.