# Solving Radical Equations and Inequalities - PowerPoint PPT Presentation

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Solving Radical Equations and Inequalities. Section 5.8. Radical Equations. Contains variable within a radical Review: How did you solve To Solve: Isolate the radical Raise both sides to a power that is equal to the index of the radical Simplify and solve

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## Solving Radical Equations and Inequalities

Section 5.8

• Contains variable within a radical

• Review: How did you solve

• To Solve:

• Raise both sides to a power that is equal to the index of the radical

• Simplify and solve

• If there are 2 radicals, set up the equation so only 1 radical is on each side of the 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.

• Raise both sides of equation to reciprocal power of given exponent

• OR rewrite equation as radical equation and solve like previous problems

• EX: Solve

• 1) 2)

• 3)

• Inequality that contains variable within radical

• Solve by using a graph & table OR algebraically

• Similar to 5.5 notes

• Graph & Table:

• Look for where Y1 = Y2 and ERROR

• Algebra:

• Solve Inequality

• 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