Question

How do I simplify 6radical 500 -3radical20+radical18?

Answer 1

$\bf 6\sqrt{500}-3\sqrt{20}+\sqrt{18}\qquad \begin{cases} 500=2\cdot 2\cdot 5\cdot 5\cdot 5\\ \qquad 2^2\cdot 5^2\cdot 5\\ \qquad (2^2\cdot 5^2)5\\ \qquad (2\cdot 5)^2 5\\ \qquad 10^2\cdot 5\\ 20=2\cdot 2\cdot 5\\ \qquad 2^2\cdot 5\\ 18=2\cdot 3\cdot 3\\ \qquad 2\cdot 3^2 \end{cases} \\\\\\ 6\sqrt{10^2\cdot 5}-3\sqrt{2^2\cdot 5}+\sqrt{2\cdot 3^2}\implies 6\cdot 10\sqrt{5}-3\cdot 2\sqrt{5}+3\sqrt{2} \\\\\\ \stackrel{like~terms}{60\sqrt{5}-6\sqrt{5}}+3\sqrt{2}\implies 54\sqrt{5}+3\sqrt{2}$