Solving Radical

Equations and Inequalities

Section 5.8

Radical Equations• Contains variable within a radical• Review: How did you solve • To Solve:

o Isolate the radicalo Raise both sides to a power that is equal to the index of the radicalo Simplify and solveo If there are 2 radicals, set up the equation so only 1 radical is on each

side of the equation

EX: Solve each equation

• 1) 2)

• 3) 4)

• 5)

Extraneous Solutions• When raising both sides of an equation to an

even power, you have to check your answers because you may get extraneous solutions.

• EX: Solve. Check your solutions.• 1) 2)

Rational Exponents• Recall: • Therefore, when you see expressions raised to

rational exponents in an equation, you can solve them using similar methods as you used for solving radical equations.o Raise both sides of equation to reciprocal power of given exponento OR rewrite equation as radical equation and solve like previous

problems

• EX: Solve• 1) 2)

• 3)

Radical Inequality• Inequality that contains variable within radical• Solve by using a graph & table OR algebraically• Similar to 5.5 notes

o Graph & Table: • Look for where Y1 = Y2 and ERROR

o Algebra: • Solve Inequality• Consider Radicand

o If even index, radicand cannot be negative

EX: Solve• Solve algebraically AND graphically.• 1) 2)

Application• The time t in seconds that it takes a car to travel

a quarter mile when starting from a full stop can be estimated by using the formula , where w is the weight of the car in pounds and p is the power delivered by the engine in horsepower. If the quarter-mile time for a 3590 lb car is 13.4 s, how much power does its engine deliver? Round to the nearest horsepower.

Homework• Pages 381-383 #27-49, 51, 58, 59, 60, 62-65