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Simplify the following:
sqrt(8) + 3 sqrt(2) + sqrt(32)

sqrt(8) = sqrt(2^3) = 2 sqrt(2):
2 sqrt(2) + 3 sqrt(2) + sqrt(32)

sqrt(32) = sqrt(2^5) = 2^2 sqrt(2):
2 sqrt(2) + 3 sqrt(2) + 2^2 sqrt(2)

2^2 = 4:
2 sqrt(2) + 3 sqrt(2) + 4 sqrt(2)

Add like terms. 2 sqrt(2) + 3 sqrt(2) + 4 sqrt(2) = 9 sqrt(2):

9 sqrt(2)

$\sqrt{8} = \sqrt{2^2 \cdot 2} = 2 \sqrt2\\ \sqrt{32} = \sqrt{4^2 \cdot 2} = 4\sqrt 2$

So

$\quad\sqrt8 + 3\sqrt 2 + \sqrt{32}\\ = 2\sqrt 2 + 3\sqrt 2 + 4\sqrt 2\\ = 9\sqrt 2$