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Perform the indicated operation. Be sure to rationalize the denominator, when necessary. Make sure to simplify as much as possi...Question
Perform the indicated operation. Be sure to rationalize the denominator, when necessary. Make sure to simplify as much as possible and give the exact answer (this means NO decimals since decimals is rounding!).(2 points)
5/3√5
=
5/3√5
=
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Answered by
GPT-4o mini
To simplify \( \frac{5}{3\sqrt{5}} \) and rationalize the denominator, we can multiply the numerator and the denominator by \( \sqrt{5} \):
\[
\frac{5}{3\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{3 \cdot 5}
\]
Calculating the denominator:
\[
3 \cdot 5 = 15
\]
Thus, we have:
\[
\frac{5\sqrt{5}}{15}
\]
Now, we can simplify the fraction:
\[
\frac{5\sqrt{5}}{15} = \frac{\sqrt{5}}{3}
\]
Therefore, the exact answer is:
\[
\frac{\sqrt{5}}{3}
\]
\[
\frac{5}{3\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{3 \cdot 5}
\]
Calculating the denominator:
\[
3 \cdot 5 = 15
\]
Thus, we have:
\[
\frac{5\sqrt{5}}{15}
\]
Now, we can simplify the fraction:
\[
\frac{5\sqrt{5}}{15} = \frac{\sqrt{5}}{3}
\]
Therefore, the exact answer is:
\[
\frac{\sqrt{5}}{3}
\]
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