Question

Simplify the following:

`sqrt(162) - sqrt(98) - sqrt(8) + sqrt(50)`

Answer 1

Given,

`sqrt(162) - sqrt(98) - sqrt(8) + sqrt(50)`

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

= `sqrt(2 xx 3 xx 3 xx 3 xx 3) - sqrt(2 xx 7 xx 7) - sqrt(2 xx 2 xx 2) + sqrt(5 xx 5 xx 2)`

= `3 xx 3sqrt(2) - 7sqrt(2) - 2sqrt(2) + 5sqrt(2)`

= `9sqrt(2) - 7sqrt(2) - 2sqrt(2) + 5sqrt(2)`

= `9 - 7 - 2 + 5sqrt(2)`

= `5sqrt(2)`

Thus, the required is `5sqrt(2)`.