# How do you simplify (7sqrt6+3sqrt7)(8sqrt6-9sqrt7)?

May 20, 2018

color(crimson)(=> 3 (49 - 13 sqrt42)

#### Explanation:

$\left(7 \sqrt{6} + .3 \sqrt{7}\right) \left(8 \sqrt{6} - 9 \sqrt{7}\right)$

$\implies 56 \cdot 6 + 24 \sqrt{42} - 63 \sqrt{42} - 27 \cdot 7$

$\implies 336 - 39 \sqrt{42} - 189$

$\implies 147 - 39 \sqrt{42}$

color(crimson)(=> 3 (49 - 13 sqrt42)