explain how the nth roots apply to geometry, algebra homework help

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Writing in Math Refer to the information on page 422 to explain how the nth roots apply to geometry. Analyze what happens to the value of r as the value of V increases.

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7-4 nth Roots Main Ideas Simplify radicals GET READY for the Lesson The radius r of a sphere with volume V can be found using the formular = This is an example of an equation that contains an nth root. In this case, n = 3. • Use a calculator to approximate radicals New Vocabulary nith root principal root Simplify Radicals Finding the square root of a number and squaring a number are inverse operations. To find the square root of a number 1, you must find a number whose square is n. Study Tip Similarly, the inverse of raising a number to the nth power is finding the wth root of a number. The table below shows the relationship between raising a number to a power and taking that root of a number Look Back Review square roots in Lesson 54. Powers Roots Factors 5.5.5 = 125 a = 125 d' = 81 = 32 3 - 3 - 3 - 3 = 81 5 is a cube root of 125 3 is a fourth root of 81. 2 is a fifth root of 32 2.2.2.2.2 = 32 0.0.0.0..... n factors of a a = b a is an ath root of b. This pattern suggests the following formal definition of an nth root KEY CONCEPT Definition of nth Root Word For any real numbers a and b, and any positive integer n, if a = b. thena is an nth root of b. Example Since 29 = 32, 2 is a fifth root of 32. The symbol V indicates an nth root. radical sign index radicand Some numbers have more than one real th root. For example, 36 has two square roots, 6 and - 6. When there is more than one real root, the nonnegative root is called the principal root. When no index is given, as in 36, the radical sign indicates the principal square root. The symbol V stands for the principal nith root of b. If is odd and bis negative, there will be no nonnegative root. In this case, the principal root is negative. 402 Chapter 7 Radical Fouations and inequalities
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