Question

Simplify the square root of 512 m3

Answer 1

$\bf \sqrt{512}\qquad \begin{cases} 512=&2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\ &2^9\\ &2^{8+1}\\ &2^{4\cdot 2+1}\\ &(2^4)^2\cdot 2^1 \end{cases}\implies \sqrt[2]{(2^4)^2\cdot 2} \\\\\\ 2^4\sqrt{2}\implies 16\sqrt{2}$