Question

the radius of a circle with an area of 60 square centimeters is represented by the expression \\(\sqrt{\frac{60}{\pi}}\\) centimeters. what is another way of expressing the radius?\
\\(\bigcirc\\) \\(2\sqrt{15\pi}\\)\
\\(\bigcirc\\) \\(4\sqrt{5\pi}\\)\
\\(\bigcirc\\) \\(\frac{2\sqrt{15\pi}}{\pi}\\)\
\\(\bigcirc\\) \\(\frac{4\sqrt{5\pi}}{\pi}\\)

Explanation:

Step1: Rationalize the denominator

$$\sqrt{\frac{60}{\pi}}=\frac{\sqrt{60}}{\sqrt{\pi}}$$
Since \(60 = 4\times15\), then \(\sqrt{60}=\sqrt{4\times15}=2\sqrt{15}\). So we have \(\frac{\sqrt{60}}{\sqrt{\pi}}=\frac{2\sqrt{15}}{\sqrt{\pi}}\).
Multiply numerator and denominator by \(\sqrt{\pi}\): \(\frac{2\sqrt{15}\times\sqrt{\pi}}{\sqrt{\pi}\times\sqrt{\pi}}=\frac{2\sqrt{15\pi}}{\pi}\)

Answer:

\(\frac{2\sqrt{15\pi}}{\pi}\) (corresponding to the third option \( \frac{2\sqrt{15\pi}}{\pi}\))