Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 612: 77

a) 3.99 ft b) 3.19 in c) 1.78 m

Work Step by Step

Radius of circle has the formula: $r = \sqrt \frac{A}{\pi}$ a) Given the Area of 50 we plug in 50 into A $r = \sqrt \frac{A}{\pi}$ $r = \sqrt \frac{50}{\pi}$ 50 can also be written as 25 x 2 because they are the two factors of 50. $r = \sqrt \frac{25 \times 2}{\pi}$ *** Square root of 25 is 5 because 5 x 5 = 25 $r = 5 \sqrt \frac{2}{\pi}$ We rewrite it as a decimal r = 3.99 ft b) Given the Area of 32 we plug in 32 into A $r = \sqrt \frac{A}{\pi}$ $r = \sqrt \frac{32}{\pi}$ 32 can also be written as 16 x 2 because they are the two factors of 32. $r = \sqrt \frac{16 \times 2}{\pi}$ *** Square root of 16 is 4 because 4 x 4 = 16 $r = 4 \sqrt \frac{2}{\pi}$ We rewrite it as a decimal r = 3.19 in c) Given the Area of 10 we plug in 10 into A $r = \sqrt \frac{A}{\pi}$ $r = \sqrt \frac{10}{\pi}$ We rewrite it as a decimal r = 1.78 m

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