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# ​ Simplify 162x3y2−−−−−√ . Assume x and y are nonnegative.

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Simplify 162x3y2−−−−−−−√ .

Assume x and y are nonnegative.

Dec 20, 2017

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Simplify sqrt(162x^3y^2)

Assume x and y are nonnegative.

$$\begin{array}{|rcll|} \hline && \sqrt{162x^3y^2} \\ &=& \sqrt{81\cdot2x^2xy^2} \\ &=& \sqrt{81x^2y^2 2x} \\ &=& \sqrt{81}\sqrt{x^2}\sqrt{y^2}\sqrt{2x} \\ &=& \sqrt{9^2}\sqrt{x^2}\sqrt{y^2}\sqrt{2x} \\ &=& 9xy\sqrt{2x} \\ \hline \end{array}$$

Dec 20, 2017