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To rationalize a denominator, you first need to understand what is rational and irrational in terms of numbers.

Rational numbers: 3, 91, $ \sqrt{9}\, $, 1

Irrational numbers: $ \pi\, $, $ \sqrt{3}\, $, 0.10100100010000...

The method to rationalizing the denominator:

If $ a < 0 $ and n is not a perfect square, then

$ \frac{a}{\sqrt{n}\,}\, * \frac{\sqrt{n}\,}{\sqrt{n}\,}\, = \frac{a\sqrt{n}\,}{n}\, $.

This works, because

$ \frac{n}{n}\, = 1 $.

Therefore, multiplying by $ \frac{\sqrt{n}\,}{\sqrt{n}\,}\, $ does not change the value of the fraction being multiplied. Hence,

$ \frac{a}{\sqrt{n}\,}\, = \frac{a\sqrt{n}\,}{n}\, $.

Now the denominator is a rational number, and you can solve it.

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