Question

How do you simplify `3sqrt8*2sqrt7`?

Answer 1

I personally multiply them so I have one number under one radical. I simplify if from there. In this case, I got `12sqrt14`.

Explanation:

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

`3sqrt8 xx 2sqrt7`

`=sqrt9sqrt8 xx sqrt4sqrt7`

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

`=sqrt72 xx sqrt28`

Again, we can multiply the numbers under the radical.

`=sqrt2016`

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:

`=sqrt144sqrt14`

We can simplify this to:

`=12sqrt14`

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

`12sqrt14 = 44.9`

`(3sqrt8)xx(2sqrt7) = 44.9`

Thus, we can conclude that `12sqrt14` is correct.

Hope this helps :)