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**Solve equations using nth roots**

EXAMPLE 4 Solve equations using nth roots Solve the equation. a. 4x5 = 128 x5 32 = Divide each side by 4. x = 32 5 Take fifth root of each side. x 2 = Simplify.

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**Solve equations using nth roots**

EXAMPLE 4 Solve equations using nth roots b. (x – 3)4 = 21 x – 3 4 + – 21 = Take fourth roots of each side. x 4 + – 21 + 3 = Add 3 to each side. x 4 21 + 3 = or – Write solutions separately. x 5.14 or 0.86 Use a calculator.

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EXAMPLE 5 Use nth roots in problem solving Biology A study determined that the weight w (in grams) of coral cod near Palawan Island, Philippines, can be approximated using the model w = ℓ 3 where l is the coral cod’s length (in centimeters). Estimate the length of a coral cod that weighs 200 grams.

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**Use nth roots in problem solving**

EXAMPLE 5 Use nth roots in problem solving SOLUTION w l 3 = Write model for weight. 200 l 3 = Substitute 200 for w. 11,976 l 3 Divide each side by 11,976 3 l Take cube root of each side. 22.9 l Use a calculator. ANSWER A coral cod that weighs 200 grams is about 23 centimeters long.

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GUIDED PRACTICE for Examples 4 and 5 Solve the equation. Round the result to two decimal places when appropriate. 16. 1 4 x3 = 2 x3 = 64 SOLUTION x = 4 SOLUTION x = 2 14. 1 2 x5 = 512 17. ( x – 2 )3 = –14 SOLUTION x = –0.41 SOLUTION x = 4 15. 3x2 = 108 18. ( x + 5 )4 = 16 SOLUTION SOLUTION x – = + 6 x = – 3 or = –7

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GUIDED PRACTICE for Examples 4 and 5 WHAT IF? Use the information from Example 5 to estimate the length of a coral cod that has the given weight. 19. a grams SOLUTION 25 cm b grams SOLUTION 27 cm c grams SOLUTION 30 cm

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