# How do you rationalize the denominator and simplify 7/(sqrt3-sqrt2)?

May 8, 2016

Multiply both numerator and denominator by $\sqrt{3} + \sqrt{2}$ to find:

$\frac{7}{\sqrt{3} - \sqrt{2}} = 7 \sqrt{3} + 7 \sqrt{2}$

#### Explanation:

Note that $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$

So: $\left(\sqrt{3} - \sqrt{2}\right) \left(\sqrt{3} + \sqrt{2}\right) = 3 - 2 = 1$

So we find:

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