# How do you simplify 6sqrt7+2sqrt28?

May 14, 2018

$\implies 10 \sqrt{7}$

#### Explanation:

We are given

$6 \sqrt{7} + 2 \sqrt{28}$

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

$= 6 \sqrt{7} + 2 \sqrt{4 \cdot 7}$

$= 6 \sqrt{7} + 2 \sqrt{{2}^{2} \cdot 7}$

$= 6 \sqrt{7} + 2 \cdot 2 \sqrt{7}$

$= 6 \sqrt{7} + 4 \sqrt{7}$

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

$= \left(6 + 4\right) \sqrt{7}$

$= 10 \sqrt{7}$

May 14, 2018

26.45751311065

#### Explanation:

$6 \sqrt{7}$ + $2 \sqrt{28}$

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:

$6 \sqrt{7}$ becomes the square root of $6 \cdot 6 \cdot 7$, which is $\sqrt{252}$. To double check, they should be the same, like this:

$6 \sqrt{7}$ = 15.87450786639
$\sqrt{252}$ = 15.87450786639

Do the same with your other square root. $2 \sqrt{28}$ is actually $2 \cdot 2$ multiplied by 28. So:

$2 \sqrt{28}$ becomes the square root of $2 \cdot 2 \cdot 28$, which is: $\sqrt{112}$. To double check:

$2 \sqrt{28}$ = 10.58300524426
$\sqrt{112}$ = 10.58300524426

Now, add your two unsimplified square roots:

$\sqrt{112}$ + $\sqrt{252}$ = 26.45751311065