# How do you simplify 6/4+ Square root of 2?

May 31, 2015

To simplify $\frac{6}{4 + \sqrt{2}}$ multiply numerator (top) and denominator (bottom) by the conjugate $\left(4 - \sqrt{2}\right)$ ...

$\frac{6}{4 + \sqrt{2}}$

$= \frac{6}{4 + \sqrt{2}} \cdot \frac{4 - \sqrt{2}}{4 - \sqrt{2}}$

$= \frac{6 \left(4 - \sqrt{2}\right)}{{4}^{2} - {\sqrt{2}}^{2}}$

$= \frac{6 \left(4 - \sqrt{2}\right)}{16 - 2}$

$= \frac{6 \left(4 - \sqrt{2}\right)}{14}$

$= \frac{3 \left(4 - \sqrt{2}\right)}{7}$

$= \frac{12 - 3 \sqrt{2}}{7}$