Question

Simplify the following:

`sqrt(48) - sqrt(12) + sqrt(75) - sqrt(27)`

Answer 1

Given,

`sqrt(48) - sqrt(12) + sqrt(75) - sqrt(27)`

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

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

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

= `4sqrt(3) - 2sqrt(3) + 5sqrt(3) - 3sqrt(3)`

= `4 - 2 + 5 - 3sqrt(3)`

= `4sqrt(3)`

Thus, the required is `4sqrt(3)`.