# How do you simplify 8 sqrt (19s) - 8 sqrt(10d) - 4 sqrt( 19s) - 8 sqrt (10d)?

$4 \sqrt{19 s} - 16 \sqrt{10 d}$

#### Explanation:

Let's first look at the terms within the square roots themselves:

$19 s$ and $10 d$

There is nothing within the roots that can be simplified - no squares under the root that can be extracted (unlike, for example, $\sqrt{4}$ which equals 2).

So what we're really talking about here is two complicated looking terms: $\sqrt{19 s}$ and $\sqrt{10 d}$ and different coefficients of them. So how about if we change the complicated looking terms and substitute in something easier to work with:

$A = \sqrt{19 s}$
$B = \sqrt{10 d}$

which gets us:

$8 A - 8 B - 4 A - 8 B$

which gives us:

$4 B - 16 B$

and now we can put in the original terms:

$4 \sqrt{19 s} - 16 \sqrt{10 d}$