Question

How do you simplify `2div (2+sqrt(2))`?

Answer 1

`2-sqrt2`

Explanation:

`"to simplify a fraction with a radical on the denominator"`

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

`"the conjugate of "a+-b" is "acolor(red)(∓)b`

`"the conjugate of "2+sqrt2" is "2color(red)(-)sqrt2`

`rArr2/(2+sqrt2)xx(2-sqrt2)/(2-sqrt2)`

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

`=(4-2sqrt2)/(4-2)=(4-2sqrt2)/2=2-sqrt2`