How do you simplify 6sqrt7+2sqrt28?

2 Answers
May 14, 2018

=>10sqrt(7)

Explanation:

We are given

6sqrt7 + 2sqrt(28)

We can factor the 28 to find a perfect square that can then be pulled out of the radical.

=6sqrt7 + 2sqrt(4*7)

=6sqrt7 + 2sqrt(2^2 * 7)

=6sqrt7 +2*2sqrt(7)

=6sqrt7 + 4sqrt(7)

Since the radicals are the same, we can combine like-terms using distribution.

=(6+4)sqrt(7)

=10sqrt(7)

May 14, 2018

26.45751311065

Explanation:

6sqrt(7) + 2sqrt(28)

First, let's unsimplify these terms in order to make 'em easier to combine. Any number that is outside the square root has a mate.

So, the 6 outside of sqrt(7) is actually 6 * 6, which is then also multiplied by 7. So:

6sqrt(7) becomes the square root of 6 * 6 * 7, which is sqrt(252). To double check, they should be the same, like this:

6sqrt(7) = 15.87450786639
sqrt(252) = 15.87450786639

Do the same with your other square root. 2sqrt(28) is actually 2 * 2 multiplied by 28. So:

2sqrt(28) becomes the square root of 2 * 2 * 28, which is: sqrt(112). To double check:

2sqrt(28) = 10.58300524426
sqrt(112) = 10.58300524426

Now, add your two unsimplified square roots:

sqrt(112) + sqrt(252) = 26.45751311065