Question

Simplify the following:

`6sqrt(72) - sqrt(18) - 8sqrt(32)`

Answer 1

Given,

`6sqrt(72) - sqrt(18) - 8sqrt(32)`

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

= `6sqrt(2 xx 2 xx 2 xx 3 xx 3) - sqrt(2 xx 3 xx 3) - 8sqrt(2 xx 2 xx 2 xx 2 xx 2)`

= `6 xx 3 xx 2sqrt(2) - 3sqrt(2) - 8 xx 2 xx 2sqrt(2)`

= `36sqrt(2) - 3sqrt(2) - 32sqrt(2)`

= `36 - 3 - 32sqrt(2)`

= `1sqrt(2)`

= `sqrt(2)`

Thus, the required is `sqrt(2)`