Solve Radical Equations

Slides:



Advertisements
Similar presentations
Warm up 1. Solve 2. Solve 3. Decompose to partial fractions -1/2, 1
Advertisements

Solving Radical Equations and Inequalities 8-8
Holt McDougal Algebra Solving Radical Equations and Inequalities Warm Up Simplify each expression. Assume all variables are positive. Write each.
College Algebra: Class 4 Radical Equations Objectives: Solve radical equations Solve equations quadratic in form Solve equations by factoring.
Solving Radical Equations and Inequalities 5-8
Remember! For a square root, the index of the radical is 2.
Solve an equation with variables on both sides
7.8 Equations Involving Radicals. Solving Equations Involving Radicals :  1. the term with a variable in the radicand on one side of the sign.  2. Raise.
Standardized Test Practice
Lesson 13.4 Solving Radical Equations. Squaring Both Sides of an Equation If a = b, then a 2 = b 2 Squaring both sides of an equation often introduces.
Solving Radical Equations and Inequalities
Objective Solve radical equations.
Section 6.6: Solve Radical Equations Starter: CC 6.5 Part 2.
Aim: How do we solve equations with fractional or negative exponents?
Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,
Warm-up Find the domain and range from these 3 equations.
WARM-UP. 8.6 PRACTICE SOLUTIONS(14-33 EVEN) CLEAR UP A FEW THINGS.
Solving Radical Equations Module 14 Topic 4.
Lesson 2- 6: Radical Functions Advanced Math Topics.
EXAMPLE 2 Rationalize denominators of fractions Simplify
Feb 9 and 10 Solving Square Root Equations. A radical equation is an equation that has a variable in a radicand (or a variable with a fractional exponent)
6.5 Solving Square Root and Other Radical Equations p390.
Other Types of Equations Solving an Equation by Factoring The Power Principle Solve a Radical Equation Solve Equations with Fractional Exponents Solve.
Other Types of Equations. Solving a Polynomial Equation by Factoring 1.Move all terms to one side and obtain zero on the other side. 2.Factor. 3. Apply.
Tom Worthing Intermediate Algebra All rights reserved. 1 Higher order equations Use Factoring method or calculator Know how many roots you will have Determine.
Solving Radical Equations Chapter 7.6. What is a Radical Equation? A Radical Equation is an equation that has a variable in a radicand or has a variable.
Solve each equation. 1. 3x +5 = x + 1 = 2x – 3 3. (x + 7)(x – 4) = 0 4.x 2 – 11x + 30 = 0 ALGEBRA O.T.Q.
Warm Up Simplify each expression. Assume all variables are positive
7.5 Solving square root and other radical equations.
Section P7 Equations. Solving Rational Equations.
7.5 Solving Radical Equations. What is a Radical Equation? A Radical Equation is an equation that has a variable in a radicand or has a variable with.
x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.
Algebra 2 Solving Radical Equations Section 7-5 Solving Square Root and Other Radical Equations Lesson 7-5.
Holt McDougal Algebra 2 Solving Radical Equations and Inequalities Solving Radical Equations and Inequalities Holt Algebra 2 Skills Check Skills Check.
4A.3 - Solving Radical Equations and Inequalities
Aim #1.6: How do we solve other types of equations?
Solving Radical Equations and Inequalities
Method: Isolate the radical (leave it alone on one side of the equal sign). Raise each side of the equation to the power suggested by the index: square,
Objective Solve radical equations..
EXAMPLE 2 Rationalize denominators of fractions Simplify
Rational Exponents and Solving Radical Equations
Essential Questions Solving Radical Equations and Inequalities
Solve a quadratic equation
Day 3 Warm-up A circular pond is modeled by the equation x2 + y2 = 225. A bridge over the pond is modeled by a segment of the equation x – 7y = – 75.
Section 1.6 Other Types of Equations
Solving Radical Equations and Inequalities
Solving Radical Equations and Inequalities 5-8
Solving Equations Containing
Essential Questions Solving Radical Equations and Inequalities
4.3 - Solving Radical Equations and Inequalities
4A.3 - Solving Radical Equations and Inequalities
3-8 Solving Radical equations
Solving Equations Containing
7.5 Solving Radical Equations
6.4 Solving Radical Equations
Solving Square Roots Unit 3 Day 3.
Solving Equations Containing
7B-1b Solving Radical Equations
Squaring a value and finding its square root is the opposite
SECTION 10-4 : RADICAL EQUATIONS
2.1 Solving Radical Equations
Bellwork. Bellwork Equations with radicals that have variables in their radicands are called radical equations. An example of a radical equation is.
Aim: How do we solve radical equations?
Solving Radical Equations and Inequalities 8-8
Objective Solve radical equations.. Objective Solve radical equations.
College Algebra 1.6 Other Equations
Section 5.8 Solving Radical Equations
Solving Equations Containing
Equations Involving Absolute Value
Section 1.6 Other Types of Equations
Presentation transcript:

Solve Radical Equations Unit 3B – Radical Functions Solve Radical Equations

A radical equation contains a variable within a radical A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.

Remember! For a square root, the index of the radical is 2.

Example 1: Solving Equations Containing One Radical Solve each equation. Check Subtract 5. Simplify. Square both sides.  Simplify. Solve for x.

Example 2: Solving Equations Containing One Radical Solve each equation. Check 3 7 7 5x - 7 84 = Divide by 7. 7 Simplify. Cube both sides.  Simplify. Solve for x.

Example 3: Solving Equations Containing Two Radicals Solve Square both sides. 7x + 2 = 9(3x – 2) Simplify. 7x + 2 = 27x – 18 Distribute. 20 = 20x Solve for x. 1 = x

You Try! Example 4 Solve each equation. Cube both sides. x + 6 = 8(x – 1) Simplify. x + 6 = 8x – 8 Distribute. 14 = 7x Solve for x. 2 = x Check 2 2 

Raising each side of an equation to an even power may introduce extraneous solutions. You don’t have to worry about extraneous solutions when solving problems to an odd power.

Example 5 Step 1 Solve for x. Square both sides. –3x + 33 = 25 – 10x + x2 Simplify. 0 = x2 – 7x – 8 Write in standard form. 0 = (x – 8)(x + 1) Factor. x – 8 = 0 or x + 1 = 0 Solve for x. x = 8 or x = –1

Example 5 Continued Method 2 Use algebra to solve the equation. Step 2 Use substitution to check for extraneous solutions. 3 –3 x 6 6  Because x = 8 is extraneous, the only solution is x = –1.

You Try! Example 6 Step 1 Solve for x. Square both sides. Simplify. 2x + 14 = x2 + 6x + 9 0 = x2 + 4x – 5 Write in standard form. Factor. 0 = (x + 5)(x – 1) x + 5 = 0 or x – 1 = 0 Solve for x. x = –5 or x = 1

You Try! Example 6 Continued Method 1 Use algebra to solve the equation. Step 2 Use substitution to check for extraneous solutions. 2 –2 x 4 4  Because x = –5 is extraneous, the only solution is x = 1.

Example 7 Method 2 Use algebra to solve the equation. Step 1 Solve for x. Square both sides. Simplify. –9x + 28 = x2 – 8x + 16 0 = x2 + x – 12 Write in standard form. Factor. 0 = (x + 4)(x – 3) x + 4 = 0 or x – 3 = 0 Solve for x. x = –4 or x = 3

Example 7 Continued Method 1 Use algebra to solve the equation. Step 2 Use substitution to check for extraneous solutions.   So BOTH answers work!!! x = –4 or x = 3

Example 8: Solving Equations with Rational Exponents Solve each equation. 1 3 (5x + 7) = 3 Cube both sides. 5x + 7 = 27 Simplify. 5x = 20 Factor. x = 4 Solve for x.

Example 9: Solving Equations with Rational Exponents 2x = (4x + 8) 1 2 Step 1 Solve for x. Raise both sides to the reciprocal power. (2x)2 = [(4x + 8) ]2 1 2 4x2 = 4x + 8 Simplify. 4x2 – 4x – 8 = 0 Write in standard form. 4(x2 – x – 2) = 0 Factor out the GCF, 4. 4(x – 2)(x + 1) = 0 Factor. 4 ≠ 0, x – 2 = 0 or x + 1 = 0 Solve for x. x = 2 or x = –1

Step 2 Use substitution to check for extraneous solutions. Example 9 Continued Step 2 Use substitution to check for extraneous solutions. 2x = (4x + 8) 1 2 2(2) (4(2) + 8) 4 16 4 4  2x = (4x + 8) 1 2 2(–1) (4(–1) + 8) –2 4 –2 2 x The only solution is x = 2.

Raise both sides to the reciprocal power. [3(x + 6) ]2 = (9)2 Example 10 1 2 3(x + 6) = 9 Raise both sides to the reciprocal power. [3(x + 6) ]2 = (9)2 1 2 9(x + 6) = 81 Simplify. 9x + 54 = 81 Distribute 9. 9x = 27 Simplify. x = 3 Solve for x.