Answer:
![2+3\sqrt{5}](https://tex.z-dn.net/?f=2%2B3%5Csqrt%7B5%7D)
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
can be simplified.
Taking prime factorization:
![=\sqrt{5^2\cdot \:3}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%5E2%5Ccdot%20%5C%3A3%7D)
which is:
![=5\sqrt{3}](https://tex.z-dn.net/?f=%3D5%5Csqrt%7B3%7D)
So an updated equation is
.
Now, we need to expand this:
First, let's expand the parenthesis:
.
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}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%5Csqrt%7B5%7D-%5Csqrt%7B5%7D%5Csqrt%7B3%7D%2B%5Csqrt%7B3%7D%5Csqrt%7B5%7D-%5Csqrt%7B3%7D%5Csqrt%7B3%7D-%5Csqrt%7B15%7D%5Csqrt%7B5%7D%2B%5Csqrt%7B15%7D%5Csqrt%7B3%7D)
And, now to simplifying!
Adding similar elements:
![\sqrt{5}\sqrt{5}-\sqrt{3}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%5Csqrt%7B5%7D-%5Csqrt%7B3%7D%5Csqrt%7B3%7D-%5Csqrt%7B15%7D%5Csqrt%7B5%7D%2B%5Csqrt%7B15%7D%5Csqrt%7B3%7D)
Simplifying and cleaning up each radical:
.
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}}](https://tex.z-dn.net/?f=%5Cboxed%7B2%2B3%5Csqrt%7B5%7D%7D)
Hope this helps!
- Sahkfam