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

1 Answer
Apr 17, 2018

2/(3-sqrt2)=color(blue)((2(3+sqrt2))/7

Explanation:

Simplify:

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

Rationalize the denominator by multiplying the numerator and denominator by $\left(3 + \sqrt{2}\right)$.

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

Simplify the denominator using FOIL
https://www.mathsisfun.com/definitions/foil-method.html.

$\frac{2 \left(3 + \sqrt{2}\right)}{9 - 2}$

$\frac{2 \left(3 + \sqrt{2}\right)}{7}$