How do you rationalize the denominator $3/(2-sqrt2)$ ?

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Answer 1 · 2015-06-02T22:36:53

Multiply both numerator (top) and denominator (bottom) by the conjugate $(2+sqrt(2))$ ...

$3/(2-sqrt(2))$

$=3/(2-sqrt(2))*(2+sqrt(2))/(2+sqrt(2))$

$=(3(2+sqrt(2)))/((2-sqrt(2))(2+sqrt(2)))$

$=(3(2+sqrt(2)))/(2^2-sqrt(2)^2)$

$=(6+3sqrt(2))/(4-2)$

$=(6+3sqrt(2))/2$

$=3+3/2sqrt(2)$

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