Problem 45 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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: \[ \frac{\sqrt{7}}{7} \].

Step 2: 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.