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see if this video helps

Guest May 3, 2017
#4
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it kinda did help thanks

#3
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I don't even know what that means

Guest May 3, 2017
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If a and b have a common non-square-number factor**, and the square root of the 2 cannot be simplified into a whole number, then $$\sqrt a$$ and $$\sqrt b$$ can be added together!!

Your question is $$\sqrt{5} + \sqrt 8$$, because 5 and 8 does not have a common non-square-number factor**, they cannot be added together. The answer is:

$$\quad\sqrt 5 + \sqrt 8 \\ =\sqrt 5 + \sqrt{2^2\cdot 2}\\ =\sqrt 5 + \sqrt{2^2} \cdot \sqrt2\\ =\sqrt 5 + 2\sqrt 2$$

Let's say $$\sqrt 8 + \sqrt {32}$$, 8 and 32 have a common non-square-number factor** 2, so they can be added together. The answer is:

$$\quad \sqrt8 + \sqrt{32}\\ =\sqrt{2^2\cdot 2}+\sqrt{2^4\cdot 2}\\ =\sqrt{2^2}\cdot \sqrt2 + \sqrt{2^4}\cdot \sqrt2\\ =2\cdot \sqrt2 + 2^2 \cdot \sqrt2\\ =2\sqrt2 + 4\sqrt2\\ =6\sqrt2$$

**: common non-square-number factor here means common factor that are not square numbers(i.e. 1,4,9,16,25,36,49,.....)

MaxWong  May 3, 2017

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