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

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Answer 1 · 2017-06-21T01:41:28

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

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 :)