# Solve: (sqrt(200x^3))/(sqrt(10x^{-1}))

Solve:
$\frac{\sqrt{200{x}^{3}}}{\sqrt{10{x}^{-1}}}$
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Given:
$\frac{\sqrt{200{x}^{3}}}{\sqrt{10{x}^{-1}}}$
Since
$\frac{\sqrt{200{x}^{3}}}{\sqrt{10{x}^{-1}}}=\sqrt{\frac{200{x}^{3}}{10{x}^{-1}}}\phantom{\rule{0ex}{0ex}}=\sqrt{\frac{10×20×{x}^{3+1}}{10}}\phantom{\rule{0ex}{0ex}}=\sqrt{20×{x}^{4}}\phantom{\rule{0ex}{0ex}}=\sqrt{4×5×{x}^{4}}\phantom{\rule{0ex}{0ex}}=\sqrt{4}\sqrt{5}\sqrt{{x}^{4}}\phantom{\rule{0ex}{0ex}}=2\sqrt{5}{x}^{2}$