Question
simplify 5/3sqrt5
Answers
GPT-4o mini
To simplify \( \frac{5}{3\sqrt{5}} \), you can rationalize the denominator. Multiply the numerator and the denominator by \( \sqrt{5} \):
\[
\frac{5}{3\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{3 \cdot 5} = \frac{5\sqrt{5}}{15}
\]
Now simplify the fraction:
\[
\frac{5\sqrt{5}}{15} = \frac{\sqrt{5}}{3}
\]
Thus, \( \frac{5}{3\sqrt{5}} \) simplifies to \( \frac{\sqrt{5}}{3} \).
\[
\frac{5}{3\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{3 \cdot 5} = \frac{5\sqrt{5}}{15}
\]
Now simplify the fraction:
\[
\frac{5\sqrt{5}}{15} = \frac{\sqrt{5}}{3}
\]
Thus, \( \frac{5}{3\sqrt{5}} \) simplifies to \( \frac{\sqrt{5}}{3} \).