Question

the square root of 49/x^3

Answer 1

\[\Large \sqrt{\frac{49}{x^3}}\]
\[\Large \frac{\sqrt{49}}{\sqrt{x^3}}\]
\[\Large \frac{\sqrt{7^2}}{\sqrt{x^2*x}}\]
\[\Large \frac{\sqrt{7^2}}{\sqrt{x^2}*\sqrt{x}}\]
\[\Large \frac{7}{x*\sqrt{x}}\]
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So far, I've shown that \[\Large \sqrt{\frac{49}{x^3}}\] turns into \[\Large \frac{7}{x*\sqrt{x}}\]
Now let's rationalize the denominator
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\[\Large \frac{7}{x*\sqrt{x}}\]
\[\Large \frac{7{\color{red}{*\sqrt{x}}}}{x*\sqrt{x}{\color{red}{*\sqrt{x}}}}\]
\[\Large \frac{7\sqrt{x}}{x*\sqrt{x*x}}\]
\[\Large \frac{7\sqrt{x}}{x*\sqrt{x^2}}\]
\[\Large \frac{7\sqrt{x}}{x*x}\]
\[\Large \frac{7\sqrt{x}}{x^2}\]
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So in the end, \[\Large \sqrt{\frac{49}{x^3}}\] simplifies to \[\Large \frac{7\sqrt{x}}{x^2}\]