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?

• \\(2\sqrt{15\pi}\\)
• \\(4\sqrt{5\pi}\\)
• \\(\frac{2\sqrt{15\pi}}{\pi}\\)
• \\(\frac{4\sqrt{5\pi}}{\pi}\\)

Explanation:

Apply the quotient property of radicals

Using the Quotient Property of Radicals knowledge point

$$ \sqrt{\frac{60}{\pi}} = \frac{\sqrt{60}}{\sqrt{\pi}} $$

Simplify the numerator radical

Using the Radical Simplification and Product Property of Radicals knowledge points

$$ \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15} $$

$$ \frac{\sqrt{60}}{\sqrt{\pi}} = \frac{2\sqrt{15}}{\sqrt{\pi}} $$

Rationalize the denominator

Using the Rationalizing the Denominator knowledge point

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

Answer:

• (A) \(2\sqrt{15\pi}\)
• (B) \(4\sqrt{5\pi}\)
• (C) \(\frac{2\sqrt{15\pi}}{\pi}\) (Correct answer)
• (D) \(\frac{4\sqrt{5\pi}}{\pi}\)