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# Rationalize the denominator

Q: Simplify the radical expression by rationalizing the denominator: $7\sqrt{100}/\sqrt{500}$. Thanks.

A: First let’s simplify the bottom, by splitting the $\sqrt{500}$ up into $\sqrt{100}*\sqrt{5}$
$7\sqrt{100}$ / $\sqrt{100}\sqrt{5}$ Â (note that $\sqrt{100}/\sqrt{100}$ = 1)
$= 7 / \sqrt{5}$

To rationalize the denominator, you just multiply by $\sqrt{5}/\sqrt{5}$. You are allowed to do this because really you are just multiplying by 1.

$7 / \sqrt{5}$
$= 7*\sqrt{5} / \sqrt{5}\sqrt{5}$

Note that $\sqrt{5}*\sqrt{5} = 5$
$= 7\sqrt{5} / 5$

There’s your answer. The denominator no longer has a square root, so it is now rationalized.