Question

What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
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Answer 1

$\sqrt{8} +3 \sqrt{2}+ \sqrt{32} =\\\\ \sqrt{4*2}+3 \sqrt{2}+ \sqrt{16*2}=\\\\2 \sqrt{2}+3 \sqrt{2}+4 \sqrt{2}=\\\\ \boxed{9 \sqrt{2} }$

Answer 2

Answer:-$\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}$ in the simplest form.

Explanation:-

Given sum :- $\sqrt{8}+3 \sqrt{2}+ \sqrt{32}$

To simplify, rewrite the numbers inside the root in the product of primes, we get

$\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}$

Thus $\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}$ in the simplest form.