Question

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

Answer 1

`216\sqrt{2}`

Explanation:

First, simplify `sqrt{12}`. We know that `12=4\cdot3` and `\sqrt{4}=2`. So we can say that `\sqrt{12}=\sqrt{4\cdot 3}` or `\sqrt{12}=\sqrt{4}\cdot\sqrt{3}`. This then simplifies to `2\sqrt{3}`.

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

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

Multiplying these two we get
`72\sqrt{18}`

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

`72\cdot 3\sqrt{2}`
`=216\sqrt{2}`

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