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# ​ Simplify. 750x15y21−−−−−√ Assume x and y are nonnegative.

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Assume x and y are nonnegative.

Dec 26, 2017

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$$7\sqrt{50x^{15}y^{21}} \\~\\ =\,7\cdot\sqrt{2\cdot5^2\cdot x\cdot x^{14}\cdot y\cdot y^{20}}$$

$$=\,7\cdot\sqrt{5^2\cdot x^{14}\cdot y^{20}\cdot2\cdot x\cdot y} \\~\\ =\,7\cdot\sqrt{5^2}\cdot \sqrt{x^{14}}\cdot \sqrt{y^{20}}\cdot\sqrt{2\cdot x\cdot y} \\~\\ =\,7\cdot5\cdot x^7\cdot y^{10}\cdot\sqrt{2xy} \\~\\ =\,35x^7y^{10}\sqrt{2xy}$$ Since  x  and  y  are not negative, we can say...

Dec 26, 2017