How do you rationalize the denominator and simplify $\frac{3}{2 - \sqrt{2}}$ $3/(2-sqrt2)$ ?

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Answer 1 · 2015-09-25T02:49:14

$\frac{6 + 3 \sqrt{2}}{2}$ $(6 + 3sqrt(2))/2$

Rationalize the denominator with the factor $(2 + \sqrt{2})$ $(2+sqrt(2))$

Hence: $\frac{3}{2 - \sqrt{2}}$ $3/(2-sqrt(2))$ = $3 \frac{(2 + \sqrt{2})}{(2 - \sqrt{2}) (2 + \sqrt{2})}$ $3((2 + sqrt(2)))/((2-sqrt2)(2+sqrt(2))$

= $3 \frac{(2 + \sqrt{2})}{4 + 2 \sqrt{2} - 2 \sqrt{2} - 2}$ $3((2+sqrt(2)))/(4+2sqrt(2)-2sqrt(2)-2)$

= $\frac{6 + 3 \sqrt{2}}{2}$ $(6 + 3sqrt(2))/2$

How do you rationalize the denominator and simplify 32−√23/(2-sqrt2)?