# How do you simplify 3sqrt8*2sqrt7?

Jun 21, 2017

I personally multiply them so I have one number under one radical. I simplify if from there. In this case, I got $12 \sqrt{14}$.

#### Explanation:

First, I square the coefficients to make it a radical.

$3 \sqrt{8} \times 2 \sqrt{7}$

$= \sqrt{9} \sqrt{8} \times \sqrt{4} \sqrt{7}$

This results in two radicals being multiplied be each other. This means that you can just multiply the number under the radical.

$= \sqrt{72} \times \sqrt{28}$

Again, we can multiply the numbers under the radical.

$= \sqrt{2016}$

Now I find a number that divides $2016$ into a whole number. The quotient must be a perfect square. $14$ works here. The quotient is $144$.

So you get:

$= \sqrt{144} \sqrt{14}$

We can simplify this to:

$= 12 \sqrt{14}$

We can double check our work by simply inputting it into our calculator and compare answers.

$12 \sqrt{14} = 44.9$

$\left(3 \sqrt{8}\right) \times \left(2 \sqrt{7}\right) = 44.9$

Thus, we can conclude that $12 \sqrt{14}$ is correct.

Hope this helps :)