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5.5 Roots of Real Numbers

5.5 Roots of Real Numbers. Alg 2. Finding the square root of a number and finding the square of a number are opposite (inverse) operations of each other. 7 2 = 49. 5 3 = 125. Some numbers have more than one real n th root. For example 36 has two square roots, 6 and -6

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5.5 Roots of Real Numbers

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  1. 5.5 Roots of Real Numbers Alg 2

  2. Finding the square root of a number and finding the square of a number are opposite (inverse) operations of each other 72 = 49 53 = 125

  3. Some numbers have more than one real nth root. For example 36 has two square roots, 6 and -6 The non-negative root is called the Principal Root Principal root Negative Principal root Both roots

  4. Radical sign Index Radicand

  5. Simplify

  6. Simplify

  7. Simplify

  8. Simplify Answer: n is even and b is negative. Thus, is not a real number. (your calculator will give you an error message “nonrealans”)

  9. Simplify. a. b. c. d. Answer: Answer: 3x4 Answer: 2xy2 Answer: not a real number

  10. Simplify Answer: Note that t is a sixth root of t6. The index is even, so the principal root is nonnegative. Since t could be negative, you must take the absolute value of t to identify the principalroot.

  11. Simplify Answer: Since the index is odd, you do not need absolute value.

  12. Original formula Physics The time T in seconds that it takes a pendulum to make a completeswing back and forth is given by the formula , where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. Find the value of T for a 1.5-foot-long pendulum. Solve Use a calculator. Answer: It takes the pendulum about 1.36 seconds to make a complete swing.

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