How do you simplify 12-15sqrt6 + 8sqrt6 - 10sqrt36?

Jun 20, 2016

$- 48 - 7 \sqrt{6}$

Explanation:

$12 - 15 \sqrt{6} + 8 \sqrt{6} - 10 \sqrt{36}$
$= 12 - 15 \sqrt{6} + 8 \sqrt{6} - 10 \sqrt{{6}^{2}}$
$= 12 - 15 \sqrt{6} + 8 \sqrt{6} - 10 \cdot 6$
$= 12 - 15 \sqrt{6} + 8 \sqrt{6} - 60$
$= 12 - 60 + \left(- 15 + 8\right) \sqrt{6}$
$= - 48 - 7 \sqrt{6}$

Jun 20, 2016

$- 48 - \left(7 \cdot \sqrt{6}\right)$

Explanation:

$12 + \left(- 15 \cdot \sqrt{6}\right) + \left(8 \cdot \sqrt{6}\right) + \left(- 10 \cdot \sqrt{36}\right)$

We know that $\sqrt{36} = 6$.

So, $12 + \left(- 15 \sqrt{6}\right) + \left(8 \cdot \sqrt{6}\right) + \left(- 60\right)$.

$12 - 60 = - 48$

So, $- 48 + \left(- 15 \sqrt{6}\right) + \left(8 \cdot \sqrt{6}\right)$

Now, take out $\sqrt{6}$ from last two parenthesis.

That would give us $- 48 + \left(\sqrt{6} \cdot \left(- 15 + 8\right)\right)$

$- 15 + 8 = - 7$

So, the answer would be $- 48 - \left(7 \cdot \sqrt{6}\right)$