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How do you simplify $\frac{6}{\sqrt{20}}$ $6/sqrt20$ ?

1 Answer

Jan 29, 2016

$\frac{6}{\sqrt{5}} = \frac{3}{5} \sqrt{5}$ $6/sqrt(5)=3/5sqrt(5)$

Explanation:

$\frac{6}{\sqrt{20}}$ $6/sqrt(20)$
$XXX = \frac{6}{\sqrt{2^{2} \times 5}}$ $color(white)("XXX")=6/sqrt(2^2xx5)$

$XXX = \frac{6}{2} \sqrt{5}$ $color(white)("XXX")=6/2sqrt(5)$

$XXX = \frac{3}{\sqrt{5}}$ $color(white)("XXX")=3/sqrt(5)$

Often when asked to simplify a fraction containing a radical, we are expected to clear the radical from the denominator;
so...
$XXX = \frac{3}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$ $color(white)("XXX")=3/sqrt(5) xx sqrt(5)/sqrt(5)$

$XXX = \frac{3 \sqrt{5}}{5}$ $color(white)("XXX")=(3sqrt(5))/5$

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