Question
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Answer
The simplified form is \( \frac{4\sqrt{15}}{25} \).
Solution
Calculate or simplify the expression \( \frac{4 \sqrt{3}}{5 \sqrt{5}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{4\sqrt{3}}{5\sqrt{5}}\)
- step1: Multiply by the Conjugate:
\(\frac{4\sqrt{3}\times \sqrt{5}}{5\sqrt{5}\times \sqrt{5}}\)
- step2: Multiply the numbers:
\(\frac{4\sqrt{15}}{5\sqrt{5}\times \sqrt{5}}\)
- step3: Multiply the numbers:
\(\frac{4\sqrt{15}}{25}\)
The simplified form of \( \frac{4 \sqrt{3}}{5 \sqrt{5}} \) is \( \frac{4\sqrt{15}}{25} \).
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Simplify this solution Extra Insights
To simplify \( \frac{4 \sqrt{3}}{5 \sqrt{5}} \), we can multiply both the numerator and the denominator by \( \sqrt{5} \) to eliminate the square root in the denominator. This gives us: \[ \frac{4 \sqrt{3} \cdot \sqrt{5}}{5 \sqrt{5} \cdot \sqrt{5}} = \frac{4 \sqrt{15}}{5 \cdot 5} = \frac{4 \sqrt{15}}{25} \] Thus, the simplified form is \( \frac{4 \sqrt{15}}{25} \).
