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EXAMPLE 4 Solve equations using nth roots Solve the equation. a. 4x 5 = 128 Divide each side by 4. x5x5 32= Take fifth root of each side. x= 32 5 Simplify. x2 =

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EXAMPLE 4 Solve equations using nth roots b. (x – 3) 4 = 21 Take fourth roots of each side. x – – 21= Add 3 to each side. x 4 + – 21+ 3= Write solutions separately. x = or x= – Use a calculator. x5.14 or x0.86

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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 = where l is the coral cods length ( in centimeters ). Estimate the length of a coral cod that weighs 200 grams.

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EXAMPLE 5 Use nth roots in problem solving SOLUTION Write model for weight. w l 3 = Substitute 200 for w l 3 = Divide each side by ,976 l 3 Take cube root of each side. 11,976 3 l Use a calculator l 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. 13. x 3 = 64 x = 4 SOLUTION x 5 = 512 SOLUTION x = x 2 = 108 SOLUTION x – = x 3 = 2 SOLUTION x= 2 17.( x – 2 ) 3 = –14 SOLUTION x = – ( x + 5 ) 4 = 16 SOLUTION x = – 3 or x = –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. 275 grams SOLUTION b. 340 grams SOLUTION 27 cm 25 cm c. 450 grams SOLUTION 30 cm

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