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?
$2sqrt{15pi}$
$4sqrt{5pi}$
$\frac{2sqrt{15pi}}{pi}$
$\frac{4sqrt{5pi}}{pi}$

Explanation:

Step1: Simplify the square - root of 60.

We know that $60 = 4\times15$, so $\sqrt{60}=\sqrt{4\times15}=2\sqrt{15}$. Then $\sqrt{\frac{60}{\pi}}=\frac{\sqrt{60}}{\sqrt{\pi}}$.

Step2: Substitute the simplified form of $\sqrt{60}$.

Since $\sqrt{60} = 2\sqrt{15}$, we have $\frac{\sqrt{60}}{\sqrt{\pi}}=\frac{2\sqrt{15}}{\sqrt{\pi}}$.

Step3: Rationalize the denominator.

Multiply the numerator and denominator by $\sqrt{\pi}$: $\frac{2\sqrt{15}}{\sqrt{\pi}}\times\frac{\sqrt{\pi}}{\sqrt{\pi}}=\frac{2\sqrt{15\pi}}{\pi}$.

Answer:

$\frac{2\sqrt{15\pi}}{\pi}$