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

Jun 23, 2016

$\frac{3}{2 - \sqrt{2}} = 3 + \frac{3}{2} \sqrt{2}$

#### Explanation:

To rationalize the denominator and simplify $\frac{3}{2 - \sqrt{2}}$, we should multiply numerator and denominator by the conjugate of denominator. As denominator is $2 - \sqrt{2}$, its conjugate is $2 + \sqrt{2}$.

$\frac{3}{2 - \sqrt{2}} = \frac{3 \times \left(2 + \sqrt{2}\right)}{\left(2 + \sqrt{2}\right) \times \left(2 - \sqrt{2}\right)}$

= $\frac{6 + 3 \sqrt{2}}{{2}^{2} - 2}$

= $\frac{6 + 3 \sqrt{2}}{4 - 2}$

= $\frac{6 + 3 \sqrt{2}}{2} = 3 + \frac{3}{2} \sqrt{2}$