Presentation on theme: "Solve equations using nth roots"— Presentation transcript:
1 Solve equations using nth roots EXAMPLE 4Solve equations using nth rootsSolve the equation.a. 4x5= 128x532=Divide each side by 4.x=325Take fifth root of each side.x2=Simplify.
2 Solve equations using nth roots EXAMPLE 4Solve equations using nth rootsb. (x – 3)4= 21x – 34+–21=Take fourth roots of each side.x4+–21+ 3=Add 3 to each side.x421+ 3=or–Write solutions separately.x5.14or0.86Use a calculator.
3 EXAMPLE 5Use nth roots in problem solvingBiologyA study determined that the weight w (in grams) of coral cod near Palawan Island, Philippines, can be approximated using the modelw = ℓ 3where l is the coral cod’s length (in centimeters). Estimate the length of a coral cod that weighs 200 grams.
4 Use nth roots in problem solving EXAMPLE 5Use nth roots in problem solvingSOLUTIONwl 3=Write model for weight.200l 3=Substitute 200 for w.11,976l 3Divide each side by11,9763lTake cube root of each side.22.9lUse a calculator.ANSWERA coral cod that weighs 200 grams is about 23 centimeters long.
5 GUIDED PRACTICEfor Examples 4 and 5Solve the equation. Round the result to two decimal places when appropriate.16.14x3 = 2x3 = 64SOLUTIONx= 4SOLUTIONx= 214.12x5 = 51217.( x – 2 )3 = –14SOLUTIONx= –0.41SOLUTIONx= 415.3x2 = 10818.( x + 5 )4 = 16SOLUTIONSOLUTIONx–= + 6x= – 3or= –7
6 GUIDED PRACTICEfor Examples 4 and 5WHAT IF? Use the information from Example 5 to estimate the length of a coral cod that has the given weight.19.a gramsSOLUTION25 cmb gramsSOLUTION27 cmc gramsSOLUTION30 cm