How do you simplify $2/(1+sqrt2)$ ?

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Answer 1 · 2015-12-03T08:10:33

$=color(blue)(2sqrt2-2$

$2/(1+sqrt2)$

We simplify this expression by rationalising the denominator.

We multiply both the numerator and the denominator by the conjugate of the denominator which is

$=color(blue)(1-sqrt2$

So,
$2/(1+sqrt2) = (2*color(blue)((1-sqrt2)))/((1+sqrt2)*(color(blue)(1-sqrt2))$

We apply the property :

$color(blue)((a+b)(a-b)=(a^2-b^2)$ , to the denominator.

$= (2 * 1-2 * sqrt2)/((1^2 - (sqrt2)^2)$

$= (2 -2sqrt2)/((1 - 2)$

$= (2 -2sqrt2)/(-1$

$=color(blue)(2sqrt2-2$

How do you simplify 2/(1+sqrt2)2/(1+sqrt2)?