# How do you simplify square root of 175 minus square root of 28?

Jul 29, 2015

$\sqrt{175} - \sqrt{28} = 3 \sqrt{7}$

#### Explanation:

First, simplify each square root:

$\sqrt{175}$, is $175$ divisible by a perfect square (other than 1)?

We could go through the list starting with ${2}^{2} = 4$ is not a factor and ${3}^{2} = 9$ is not a factor, and when we get to ${5}^{2} = 25$, we find that:

$175 = 25 \times 7$

So $\sqrt{175} = \sqrt{25 \times 7} = \sqrt{25} \times \sqrt{7} = 5 \sqrt{7}$.

We cannot further simplfy $\sqrt{7}$ so we'll simplify the other square root.

$28 = 4 \times 7$, so we get:

$\sqrt{28} = \sqrt{4 \times 7} = 2 \sqrt{7}$

Here's the short way to write what we've done:

$\sqrt{175} - \sqrt{28} = \sqrt{25 \times 7} - \sqrt{4 \times 7}$

$= 5 \sqrt{7} - 2 \sqrt{7}$

Now, if we have 5 of these things and we subtract 2 of the things, surely we end up with 3 of the things.

So:

$\sqrt{175} - \sqrt{28} = 5 \sqrt{7} - 2 \sqrt{7}$

$= 3 \sqrt{7}$