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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}  (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.