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I'm having a lot of trouble figuring out how to evaluate this problem:

$$\dfrac{7}{\frac{7\sqrt{85}}{85}}$$

Everything I've found says that the answer is just $1\sqrt{85}$, but I have no idea how to get there. The best thing I can figure out how to do is to cut it down to $$7 \cdot \frac{85}{7\sqrt{85}}$$

Can anyone help me with this? Thank you!

Jyrki Lahtonen
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Conor
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1 Answers1

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$7 \div {\frac{7\sqrt{85}}{85}}=7 * \frac{85}{7\sqrt{85}}=\frac{85}{\sqrt{85}}=\sqrt{85}$

Basically this is just a game of cancelling from numerator and denominator.

Cbjork
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    For the OP's benefit: $\dfrac a{\sqrt a}=\sqrt a$ for all $a$. This can be shown by rationalizing the denominator, or by taking the equation $a=\sqrt a\sqrt a$ and dividing both sides by $\sqrt a$. – Akiva Weinberger Apr 07 '15 at 19:11