Question

Simplify the following:

`sqrt(75) - sqrt(12) + sqrt(27)`

Answer 1

Given,

`sqrt(75) - sqrt(12) + sqrt(27)`

Convert the surds in simplest form by finding the prime factors of each surd.

= `sqrt(5 xx 5 xx 3) - sqrt(2 xx 2 xx 3) + sqrt(3 xx 3 xx 3)`

= `5sqrt(3) - 2sqrt(3) + 3sqrt(3)`

= `5 - 2 + 3sqrt(3)`

= `6sqrt(3)`

Thus, the required is `6sqrt(3)`.