Question

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

Answer 1

`\bf 6√(500)-3√(20)+√(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√(10^2\cdot 5)-3√(2^2\cdot 5)+√(2\cdot 3^2)\implies 6\cdot 10√(5)-3\cdot 2√(5)+3√(2) \\\\\\ \stackrel{like~terms}{60√(5)-6√(5)}+3√(2)\implies 54√(5)+3√(2)`