Question

How do you simplify `6sqrt7+2sqrt28`?

Answer 1

`=>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)`

Answer 2

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