How do you rationalize the denominator $\sqrt{\frac{x}{5}}$ $sqrt(x/5)$ ?

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Answer 1 · 2018-04-17T04:25:27

The rationalized fraction is $\frac{\sqrt{5 x}}{5}$ $sqrt(5x)/5$ .

Split the radical:

$= \sqrt{\frac{x}{5}}$ $color(white)=sqrt(x/5)$

$= \frac{\sqrt{x}}{\sqrt{5}}$ $=sqrtx/sqrt5$

Then multiply the top and bottom by $\sqrt{5}$ $sqrt5$ :

$= \frac{\sqrt{x}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$ $=sqrtx/sqrt5color(red)(*sqrt5/sqrt5)$

$= \frac{\sqrt{x} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}}$ $=(sqrtx*sqrt5)/(sqrt5*sqrt5)$

$= \frac{\sqrt{x} \cdot \sqrt{5}}{{(\sqrt{5})}^{2}}$ $=(sqrtx*sqrt5)/((sqrt5)^2)$

$= \frac{\sqrt{x} \cdot \sqrt{5}}{5}$ $=(sqrtx*sqrt5)/5$

$= \frac{\sqrt{x \cdot 5}}{5}$ $=(sqrt(x*5))/5$

$= \frac{\sqrt{5 x}}{5}$ $=sqrt(5x)/5$

That's it. Hope this helped!

How do you rationalize the denominator √x5sqrt(x/5)?