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Chapter 0: Problem 45

Rationalize the denominator. $$\frac{1}{\sqrt{7}}$$

Short Answer

Expert verified
\(\frac{\sqrt{7}}{7}\)

Step by step solution

01

Rationalize the Denominator

In order to rationalize the denominator, multiply both numerator and denominator of the given fraction by the denominator, \( \sqrt{7} \). This gives: \[ \frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} \] which simplifies to: \[ \frac{\sqrt{7}}{7} \].
02

Simplify the Expression

At this step, you have rationalized the denominator, and the expression is simplified. The square root of 7 is the simplified form of \(\sqrt{7}\) and 7 is just \( \sqrt{7} \times \sqrt{7} \). So, \[ \frac{\sqrt{7}}{7} \] is the final, simplified, and rationalized expression.

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Most popular questions from this chapter

Evaluate each expression without using a calculator. $$16^{-\frac{5}{2}}$$

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