Question

simplify this surds by showing your answer to prove it...
1). √5+√8-√20+√2=
2.) -6√20+2√45+7√5=
please help....
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Answer 1

The main idea is that you can take squares out of a square root:

$\sqrt{a^2}=a$

Along with the multiplication property

$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

So, we have

$\sqrt{8}=\sqrt{4\cdot 2}=\sqrt{4}\cdot\sqrt{2}=2\sqrt{2}$

$\sqrt{20}=\sqrt{4\cdot 5}=\sqrt{4}\cdot\sqrt{5}=2\sqrt{5}$

$\sqrt{45}=\sqrt{9\cdot 5}=\sqrt{9}\cdot\sqrt{5}=3\sqrt{5}$

The first sum becomes

$\sqrt{5}+2\sqrt{2}-2\sqrt{5}+\sqrt{2}=3\sqrt{2}-\sqrt{5}$

And the second becomes

$-6(2\sqrt{5})+2(3\sqrt{5})+7\sqrt{5}=-12\sqrt{5}+6\sqrt{5}+7\sqrt{5}=\sqrt{5}$