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Rationalize the denominator. \(\frac{13}{\sqrt{40}}\)

Short Answer

Expert verified
The rationalized form of \( \frac{13}{\sqrt{40}} \) is \( \frac{13\sqrt{10}}{20} \).

Step by step solution

01

Identify the Denominator

The denominator we wish to rationalize is \(\sqrt{40}\)
02

Simplify the Denominator

The first step, to simplify the denominator, is to rewrite \(\sqrt{40}\) as \(\sqrt{4*10}\). This simplifies further to \(2\sqrt{10}\). The reasoned behind breaking 40 down that way is because 4 is a perfect square and can be square rooted cleanly.
03

Multiplying by a Form of 1

To rationalise the denominator, multiply the expression by a certain form of 1—in this case \( \frac{\sqrt{10}}{\sqrt{10}}\)—such that the denominator will become a rational number. This then gives us \( \frac{13\sqrt{10}}{20} \) as our final simplified expression.

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