the radius of a circle with an area of 60 square centimeters is represented by the expression…

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

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

Answer

Explanation:

Step1: Simplify the square - root of the fraction

We know that $\sqrt{\frac{60}{\pi}}=\frac{\sqrt{60}}{\sqrt{\pi}}$.

Step2: Simplify the numerator $\sqrt{60}$

Factorize 60: $60 = 4\times15$, so $\sqrt{60}=\sqrt{4\times15}=\sqrt{4}\times\sqrt{15}=2\sqrt{15}$.

Step3: Rationalize the denominator

$\frac{\sqrt{60}}{\sqrt{\pi}}=\frac{2\sqrt{15}}{\sqrt{\pi}}$. Multiply the numerator and denominator by $\sqrt{\pi}$ to get $\frac{2\sqrt{15}\times\sqrt{\pi}}{\sqrt{\pi}\times\sqrt{\pi}}=\frac{2\sqrt{15\pi}}{\pi}$.

Answer:

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