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

Dec 3, 2015

=color(blue)(2sqrt2-2

#### Explanation:

$\frac{2}{1 + \sqrt{2}}$

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