Question

Simplify the following:

`3sqrt(11) + 8sqrt(99) - sqrt(44)`

Answer 1

Given,

`3sqrt(11) + 8sqrt(99) - sqrt(44)`

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

= `3sqrt(11) + 8sqrt(3 xx 3 xx 11) - sqrt(2 xx 2 xx 11)`

= `3sqrt(11) + 8 xx 3sqrt(11) - 2sqrt(11)`

= `3 + 24 - 2sqrt(11)`

= `25sqrt(11)`

Thus, the required is `25sqrt(11)`.