WILL MARK BRAINLIEST. PLEASE HELP.
simplify:
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Answer:
[tex]2+3\sqrt{5}[/tex]
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 [tex]\sqrt{75}[/tex] can be simplified.
Taking prime factorization:
[tex]=\sqrt{5^2\cdot \:3}[/tex]
which is:
[tex]=5\sqrt{3}[/tex]
So an updated equation is [tex]\left(\sqrt{5}+\sqrt{3}-\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)+5\sqrt{3}[/tex].
Now, we need to expand this:
First, let's expand the parenthesis:
[tex]\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)[/tex].
We can apply some of are rules:
[tex]\sqrt{5}\sqrt{5}-\sqrt{5}\sqrt{3}+\sqrt{3}\sqrt{5}-\sqrt{3}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}[/tex]
And, now to simplifying!
Adding similar elements:
[tex]\sqrt{5}\sqrt{5}-\sqrt{3}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}[/tex]
Simplifying and cleaning up each radical:
[tex]5-3-5\sqrt{3}+3\sqrt{5}[/tex].
Now all we have to do is add the similar elements (again.)
In doing so we reach an answer of [tex]\boxed{2+3\sqrt{5}}[/tex]
Hope this helps!
- Sahkfam