Question
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Answer
The simplified form is \( \frac{8\sqrt{5}}{21} \).
Solution
To simplify √(320/441):
Step 1: Write the square root as a fraction of square roots.
√(320/441) = √320 / √441
Step 2: Simplify each square root individually.
√441 = 21 (since 21 × 21 = 441)
For √320, factor 320:
320 = 64 × 5
√320 = √(64 × 5) = √64 × √5 = 8√5
Step 3: Combine the results.
√(320/441) = (8√5) / 21
Final Answer:
8√5/21
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Simplify this solution Extra Insights
To simplify \( \sqrt{\frac{320}{441}} \), we can find the square root of both the numerator and the denominator separately. The numerator can be factored: \( 320 = 64 \times 5 = 16 \times 20 = 16 \times 4 \times 5 = 4^2 \times 5 \). Hence, \( \sqrt{320} = 4\sqrt{5} \). The denominator simplifies as \( 441 = 21^2 \), therefore \( \sqrt{441} = 21 \). Now putting it together, we have: \[ \sqrt{\frac{320}{441}} = \frac{\sqrt{320}}{\sqrt{441}} = \frac{4\sqrt{5}}{21} \] So, the final answer is: \[ \frac{4\sqrt{5}}{21} \]
