Question

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

Answer 1

`\bf √(8)+3√(2)+√(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} \\\\\\ √(2^2\cdot 2)+3√(2)+√((2^2)^2\cdot 2)\implies 2√(2)+3√(2)+2^2√(2) \\\\\\ \stackrel{like-terms}{2√(2)+3√(2)+4√(2)}\implies 9√(2)`