Download presentation

1
**Solving Radical Equations and Inequalities**

Algebra II January 24 & 25

2
**Evaluate the following expressions.**

Warm - Up Evaluate the following expressions. 1. 2. Solution: 16 Solution: - 8

3
Radicals/Exponents What does it mean when you have a fractions as an exponent? Such as: What this stands for is: the number in the numerator is the power, and the number in the denominator is the radical power. So I could write this in another way like:

4
**Write each statement in a different form than given.**

1. 2. 3.

5
**What about negative exponents**

What about negative exponents? Remember negative exponent means your doing the inverse.

6
**Write each statement in a different form than given.**

1. 2. 3.

7
**Solve the following rational exponential equation:**

Rational Exponents Solve the following rational exponential equation: OPTION #1 Step 1: Convert from exponent to radical form: Step 2: eliminate the radical: Step 3: Simplify:

8
**Solve the following rational exponential equation:**

Rational Exponents Solve the following rational exponential equation: OPTION #2 Step 1: Raise to the reciprocal power of the original power: Step 2: Simplify:

9
**Solving Radical Equations**

A radical equation is an equation with one or more radicals that have variables in their radicand. Solving Radical Equations Steps Step 1 Isolate the radical on one side of the equation if necessary. Step 2 Raise each side of the equation to the same power to get rid of the radical. Step 3 Solve the equation and check your solution.

10
**Solve a radical Equation**

Write original equation. Cube each side. Simplify. Subtract 7 from each side. x = 10 Divide each side by 2. Solution x = 10 Check.

11
**Try These… 1. SOLUTION: x = 512 2. SOLUTION: x = -9 3.**

12
**Rational Exponent Example**

What is the solution of the equation Write original equation. Divide each side by 3. Raise each side to the power of 3/2. x = 64 Simplify. Solution x = 64 Check.

13
**Solve an equation with a rational Exponent.**

Write original equation. Add 1 to each side. Raise each side to the power of 4/3. Apply exponent properties. x = 14 Solve the equation. Solution x = 14 Check.

14
Try These… 1. 2. 3. SOLUTION: x = 25 SOLUTION: x = 1 SOLUTION: x = 6

15
**Solve an equation w/ an extraneous solution**

Write original equation. Square each side. FOIL the left side and simplify the right. Write in standard form. Factor. x = 7 or x = -2 Solve. x = 7 (The -2 is extraneous) Check.

16
**Solve an equation with 2 radicals**

METHOD 1 Write original equation. Square each side. FOIL the left side and simplify the right. Isolate the radical. Divide both sides by 2 . Square each side again. Simplify. Write in standard form and factor. x = 2 or x = -1 Solve. x = -1 (The 2 is extraneous) Check.

17
**Solve an equation with 2 radicals**

METHOD 2 Write original equation. Graph y1 = Graph y2 = Find the point of intersection! You will find that the ONLY point of intersection is (-1, 2). Therefore, -1 is the only solution of the equation.

18
**Try These… Solve the equation. Check for extraneous solutions.**

1. 2. 3. SOLUTION: x = 1 SOLUTION: x = 0, 4 SOLUTION: x = 3

19
**Solve radical inequalities**

Use a graph to solve SOLUTION Step 1 ENTER the function and y = 3 into the graphing calculator. Step 2 GRAPH the functions from Step 1. Step 3 Identify the x-values for which the graph of lies above the graph of y = 3. SOLUTION: x > 14

20
**Solve the following radical inequalities (try by hand)**

1. 2. SOLUTION: x > 32 SOLUTION: x ≥ 16

21
Class Work p. 447 #3-23 odd p. 456 #5, 7, 13, 17, 23, 27, 37, 45

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google