Newton Simpson
06/05/2023 · Junior High School
Which expression is equivalent to \( \frac{3 \sqrt{20}}{\sqrt{54}} \) ?
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \frac{3 \sqrt{20}}{\sqrt{54}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{3\sqrt{20}}{\sqrt{54}}\)
- step1: Simplify the root:
\(\frac{3\times 2\sqrt{5}}{\sqrt{54}}\)
- step2: Simplify the root:
\(\frac{3\times 2\sqrt{5}}{3\sqrt{6}}\)
- step3: Multiply the terms:
\(\frac{6\sqrt{5}}{3\sqrt{6}}\)
- step4: Reduce the fraction:
\(\frac{2\sqrt{5}}{\sqrt{6}}\)
- step5: Multiply by the Conjugate:
\(\frac{2\sqrt{5}\times \sqrt{6}}{\sqrt{6}\times \sqrt{6}}\)
- step6: Multiply the numbers:
\(\frac{2\sqrt{30}}{\sqrt{6}\times \sqrt{6}}\)
- step7: Multiply the numbers:
\(\frac{2\sqrt{30}}{6}\)
- step8: Reduce the fraction:
\(\frac{\sqrt{30}}{3}\)
The expression \( \frac{3 \sqrt{20}}{\sqrt{54}} \) is equivalent to \( \frac{\sqrt{30}}{3} \).
Quick Answer
\( \frac{\sqrt{30}}{3} \)
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