# How do you simplify 4*sqrt(12) * (9 sqrt(6))?

Apr 27, 2017

$216 \setminus \sqrt{2}$

#### Explanation:

First, simplify $\sqrt{12}$. We know that $12 = 4 \setminus \cdot 3$ and $\setminus \sqrt{4} = 2$. So we can say that $\setminus \sqrt{12} = \setminus \sqrt{4 \setminus \cdot 3}$ or $\setminus \sqrt{12} = \setminus \sqrt{4} \setminus \cdot \setminus \sqrt{3}$. This then simplifies to $2 \setminus \sqrt{3}$.

Now we have
$4 \setminus \cdot 2 \setminus \sqrt{3} \setminus \cdot 9 \setminus \sqrt{6}$

We can simplify this to
$8 \setminus \sqrt{3} \setminus \cdot 9 \setminus \sqrt{6}$

Multiplying these two we get
$72 \setminus \sqrt{18}$

We know that $18 = 9 \setminus \cdot 2$ so we can do the following
$\setminus \sqrt{18} = \setminus \sqrt{9 \setminus \cdot 2} = 3 \setminus \sqrt{2}$

$72 \setminus \cdot 3 \setminus \sqrt{2}$
$= 216 \setminus \sqrt{2}$

Since 2 is a prime number, we can't simplify anymore.
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