Question

What is the following in simplest form? sqrt(8)+3sqrt(2)+sqrt(32)

Answer 1

$\bf \sqrt{8}+3\sqrt{2}+\sqrt{32}\qquad \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2\\ 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^4\cdot 2\\ \qquad (2^2)^2\cdot 2 \end{cases} \\\\\\ \sqrt{2^2\cdot 2}+3\sqrt{2}+\sqrt{(2^2)^2\cdot 2}\implies 2\sqrt{2}+3\sqrt{2}+2^2\sqrt{2} \\\\\\ \stackrel{like-terms}{2\sqrt{2}+3\sqrt{2}+4\sqrt{2}}\implies 9\sqrt{2}$