Question
Rationalize the denominator. \( \frac{3 \sqrt{2}}{\sqrt{7}} \) \( \frac{3 \sqrt{2}}{\sqrt{7}}=\square \) (Type an exact answer, using radicals as needed.)
Ask by Hobbs Stephens. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{3 \sqrt{14}}{7}
\]
Solution
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The Deep Dive
To rationalize the denominator of \( \frac{3 \sqrt{2}}{\sqrt{7}} \), you multiply both the numerator and the denominator by \( \sqrt{7} \): \[ \frac{3 \sqrt{2}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = \frac{3 \sqrt{2} \cdot \sqrt{7}}{7} = \frac{3 \sqrt{14}}{7}. \] Thus, the expression with a rationalized denominator is \( \frac{3 \sqrt{14}}{7} \). So, \[ \frac{3 \sqrt{2}}{\sqrt{7}}=\frac{3 \sqrt{14}}{7}. \]
