Question

How do you simplify `8/(3 + sqrt2)`?

Answer 1

`1/7(24-8sqrt2)`

Explanation:

`"multiply the numerator/denominator by the "color(blue)"conjugate"`
`"of the denominator"`

`"the conjugate of "3+sqrt2" is "3color(red)(-)sqrt2`

`=(8(3-sqrt2))/((3+sqrt2)(3-sqrt2))`

`=(24-8sqrt2)/(3^2-(sqrt2)^2)`

`=(24-8sqrt2)/7=1/7(24-8sqrt2)`