Solving Radical Equations 3 Solve the equation: 2 2π₯ β 3 β 22 = 0 3 2 2π₯ β 3 = 22 3 Isolate the radical 3 2π₯ β 3 = 11 Isolate the radical 2π₯ β 3 3 = 11 3 2π₯ β 3 = 1331 2π₯ = 1334 π₯ = 667 Cube both sides Simplify Solve for x 4 4 Solve the equation: 4π₯ + 3 = 2 π₯ β 1 4 4π₯ + 3 4 4 = 2 π₯β1 4 Raise each side to the 4th power 4π₯ + 3 = 16(π₯ β 1) Simplify 4π₯ + 3 = 16π₯ β 16 Distribute 19 = 12π₯ Solve for x 19 π₯= 12 Solve the equation: 5 (2π₯ + 2)2 5 5 = 3 (2π₯ + 2)2 = 3 5 Raise each side to the 5th power (2π₯ + 2)2 = 243 Simplify (2π₯ + 2)2 = 243 Square root 2π₯ + 2 = 15.588 Simplify 2π₯ = 13.588 π₯ β 6.794 Solve for x Solve the equation: 5 (2π₯ + 2)2 = 3 (2π₯ + 2)2/5 = 3 ((2π₯ + 2)2/5 )5/2 = (3)5/2 2π₯ + 2 = 15.588 2π₯ = 13.588 Re-write exponent as a fraction Raise to the reciprocal power Simplify Solve for x π₯ β 6.794 Alternative method using fractions as exponents. π πβ r= Solve for V: 2 π = π πβ π2 π = πβ 2 πβπ 2 = π Square each side Simplify Multiply by Οh π πβ r= Solve for h: 2 π = π πβ π2 π = πβ 2 Square each side Simplify π = π Multiply by h π β= 2 ππ Multiply by r2 βπ 2 T = 2π Solve for m: π = 2π π 2π 2 = π π π π π π Isolate the square root 2 Square both sides π2 π = 2 4π π Simplify π2π =π 2 4π Multiply by k M = 2π Solve for P: 3 π ππ = 2π πΏ ππΏ = 2π ππΏ 2π 3 = 3 ππ ππ πΏ Isolate the cube root: divide by 2Ο ππ 3 3 Isolate the cube root: mult. by L 3 Cube both sides π3 πΏ3 = ππ 3 8π Simplify π3 πΏ3 =π 3 8π π Divide by k The time T in seconds for a pendulum to complete one back-andforth swing is given by π = 2π πΏ 9.9 , where L is the length of the pendulum in meters. Find the length of a pendulum that completes one back-and-forth swing in 2.2 seconds. π 2π = 2π = πΏ 9.9 π2 πΏ = 2π 9.9 9.9π 2 =πΏ 2π 9.9(2.2)2 2π Isolate the square root 2 2 π πΏ 9.9 Square both sides Simplify Isolate L = πΏ, πΏ β 7.626 πππ‘πππ Substitute for T, solve
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