# How do you rationalize the denominator and simplify 2/(sqrt3+sqrt2)?

Mar 26, 2016

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

#### Explanation:

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

We rationalise the expression by multiplying it with the conjugate of the denominator.

Conjugate of color(blue)(sqrt3 + sqrt 2= sqrt 3 - sqrt2

(2 * color(blue)((sqrt 3 - sqrt2))) / ((sqrt3 + sqrt2) * color(blue)((sqrt 3 - sqrt2))

• Applying property :- color(green)((a+b)(a-b) = a^2 - b^2, to the denominator.

 =(2 * color(blue)((sqrt 3)) + 2 * color(blue)( (- sqrt2))) / ((sqrt3)^2 - (sqrt2)^2

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

$= \frac{2 \left(\sqrt{3} - \sqrt{2}\right)}{1}$

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