Question

How do you simplify: `(sqrt2+ 2sqrt2 +sqrt8) /sqrt3`?

Answer 1

`(sqrt2+2sqrt2+sqrt8)/sqrt3=5/3sqrt6`

Explanation:

As we have a surd in the denominator, here simplifying means rationalizing the denominator, which can be done by multiplying numerator and denominator by `sqrt3`.

Hence `(sqrt2+2sqrt2+sqrt8)/sqrt3`

= `(sqrt2+2sqrt2+sqrt(ul(2xx2)xx2))/sqrt3`

= `(sqrt2+2sqrt2+2sqrt2)/sqrt3`

= `(5sqrt2)/(sqrt3)xx(sqrt3)/(sqrt3)`

= `(5sqrt6)/3`

= `5/3sqrt6`

Answer 2

`sqrt8=sqrt4sqrt2=2sqrt2`

`[sqrt2+2sqrt2+2sqrt2]/sqrt3`

Collect like terms

`[5sqrt2]/(sqrt3)`

Rationalise the denominator

`[5sqrt2]/(sqrt3)xxsqrt3/sqrt3`

`[5sqrt6]/3`