Friday, 2 August 2013

algebra precalculus - Simplify this expression fully



How would i simplify fully the following expression?




$\dfrac{{\sqrt 2}({x^3})}{\sqrt{\frac {32}{x^2}}}$



So far i have got this



$\dfrac{{\sqrt 2}{x^3}}{{\frac{\sqrt 32}{\sqrt x^2}}}$ = $\dfrac{{\sqrt 2}{x^3}}{{\frac{4\sqrt 2}{x}}}$



Am not quite sure if this is correct however, could someone help explain how i would simplify this expression?


Answer



There is a mistake in the OP. Recall that $\sqrt{x^2}=|x|\ne x$ when $x<0$. To simplify, we can write




$$\frac{\sqrt 2 x^3}{\sqrt{\frac{32}x}}=\frac{\sqrt 2 x^3}{\frac{4\sqrt 2}{|x|}}=\frac{x^3|x|}{4}$$


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