Question

How do you rationalize the denominator and simplify `5/(sqrt14-2)`?

Answer 1

`\frac{5\sqrt{14}+10}{10}`

Explanation:

Use the identity `(a-b)(a+b)=a^2-b^2` in the following way:

`\frac{5}{\sqrt{14}-2} = \frac{5}{\sqrt{14}-2} \cdot 1 = \frac{5}{(\sqrt{14}-2)} \cdot \frac{(\sqrt{14}+2)}{(\sqrt{14}+2)}`

Now, the numerator is simply `5(\sqrt{14}+2) = 5\sqrt{14}+10`, while at the denominator we have the forementioned identity:

`(\sqrt{14}-2)(\sqrt{14}+2) = (\sqrt{14})^2 - 2^2 = 14-4 = 10`