Question

How do you rationalize the denominator and simplify `3/(2-sqrt2)`?

Answer 1

`3/(2-sqrt2)=3+3/2sqrt2`

Explanation:

To rationalize the denominator and simplify `3/(2-sqrt2)`, we should multiply numerator and denominator by the conjugate of denominator. As denominator is `2-sqrt2`, its conjugate is `2+sqrt2`.

`3/(2-sqrt2)=(3xx(2+sqrt2))/((2+sqrt2)xx(2-sqrt2))`

= `(6+3sqrt2)/(2^2-2)`

= `(6+3sqrt2)/(4-2)`

= `(6+3sqrt2)/2=3+3/2sqrt2`