Question

WILL MARK BRAINLIEST. PLEASE HELP. simplify:

Answer 1

Answer:

$2+3\sqrt{5}$

Step-by-step explanation:

Hi!

This is a lot of radicals, so it may seem tricky. Let's begin by simplifying all of the radicals that can be simplified.

We can see that $\sqrt{75}$ can be simplified.

Taking prime factorization:

$=\sqrt{5^2\cdot \:3}$

which is:

$=5\sqrt{3}$

So an updated equation is $\left(\sqrt{5}+\sqrt{3}-\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)+5\sqrt{3}$.

Now, we need to expand this:

First, let's expand the parenthesis:

$\sqrt{5}\sqrt{5}+\sqrt{5}\left(-\sqrt{3}\right)+\sqrt{3}\sqrt{5}+\sqrt{3}\left(-\sqrt{3}\right)+\left(-\sqrt{15}\right)\sqrt{5}+\left(-\sqrt{15}\right)\left(-\sqrt{3}\right)$.

We can apply some of are rules:

$\sqrt{5}\sqrt{5}-\sqrt{5}\sqrt{3}+\sqrt{3}\sqrt{5}-\sqrt{3}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}$

And, now to simplifying!

Adding similar elements:

$\sqrt{5}\sqrt{5}-\sqrt{3}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}$

Simplifying and cleaning up each radical:

$5-3-5\sqrt{3}+3\sqrt{5}$.

Now all we have to do is add the similar elements (again.)

In doing so we reach an answer of $\boxed{2+3\sqrt{5}}$

Hope this helps!

- Sahkfam