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 :)

How do you simplify 3sqrt8*2sqrt73sqrt8*2sqrt7?