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A homework question recently asked for me to simplify:

$\frac{1}{\sqrt{7}} \div {7}$

It's easy to see that this becomes

$\frac{1}{7\sqrt{7}}$

But according to wolfram alpha this is also equal to $\frac{\sqrt{7}}{49}$.

What sequence of steps can I use to get the second representation of this quantity from the first?

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    $\begingroup$ $$\frac{1}{7\sqrt{7}}\cdot \frac{\sqrt{7}}{\sqrt{7}}.$$ $\endgroup$ – Daniel Fischer Dec 8 '13 at 14:52
  • $\begingroup$ Multiply both numerator and denominator bt Sqrt[7] and simplify the denominator [7 Sqrt(7) Sqrt(7)] = 7 7 = 49 $\endgroup$ – Claude Leibovici Dec 8 '13 at 14:52
  • $\begingroup$ If you replace 7 by x, you have the same solution $\endgroup$ – Claude Leibovici Dec 8 '13 at 15:04
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$\dfrac{1}{\sqrt{7}}\div7=\dfrac{1}{7\sqrt{7}}=\dfrac{1}{7\sqrt{7}}\cdot\dfrac{\sqrt{7}}{\sqrt{7}}=\dots$

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$$\frac{1}{7\sqrt{7}} =\frac{\sqrt{7}}{7\sqrt{7}\cdot\sqrt{7}}=\frac{\sqrt{7}}{7\cdot7}=\frac{\sqrt{7}}{49}$$

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This is called denominator rationalization. You multiply numerator and denominator with the same root, so you effectively move from denominator into the numerator.

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