S OLVING R ADICAL E QUATIONS Objective: solve simple radical equations and check for extraneous solutions How do you undo a square root or a cube root?

Slides:

Advertisements

Similar presentations

Solving Radical Equations. The simplest kind of radical equation is one like this.

Advertisements

5.7 Rational Exponents 5.8 Radical equations

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

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.

Radical Equations: KEY IDEAS An equation that has a radical with a variable under the radicand is called a radical equation. The only restriction on to.

Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).

Chapter 2: Equations and Inequalities 2.4: Other Types of Equations

Solving Radical Equations

Solving Equations Containing To solve an equation with a radical expression, you need to isolate the variable on one side of the equation. Factored out.

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.

Section 6.6: Solve Radical Equations Starter: CC 6.5 Part 2.

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.

Remember that exponential functions and logarithmic functions are inverses of each other. We will use this property to solve problems.

Solving equations Section 1.4.

6.4 R ATIONAL E XPONENTS 6.5 S OLVING S QUARE R OOT AND O THER R ADICAL E QUATIONS Algebra II w/ trig.

6.6 Solving Radical Equations. Principle of power: If a = b then a n = b n for any n Question: Is it also true that if a n = b n then a = b? Explain in.

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.

Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root.

Unit 7 Quadratics Radical Equations Goal: I can solve simple radical equations in one variable (A-REI.2)

Solving One Step Equations Notes and Practice Problems.

Chapter 7 Day 3 Book Section 7.5 Get 2 grids for the 2 shift problems!

Get radical alone. 5 Tues 1/12 Lesson 6 – 5 Learning Objective: To solve radical equations Hw: Lesson 6 – 5 WS 2.

Mon 1/11 Lesson 6 – 5 Learning Objective: To solve square root equations Hw: Lesson 6 – 5 WS 1.

Notes Over 7.6 Solving a Simple Radical Equation Solve the equation. Check your solution.

7.5 Solving Radical Equations Objective: Be able to solve square root equations and other radical equations.

+ 2 –10 –3 –5 2 ( )( ) – 5 Check using FOIL ( )( ) Factor If you factor out a GMF: before using the X figure, keep it, after using the.

Mr. Morris duPont Manual High School.  First, we need to know the generic graph of We can always graph two points easily (0,0)and (1, a ) Graphing Root.

Section P7 Equations. Solving Rational Equations.

A radical equation is an equation that contains a radical. BACK.

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.

Radical Equation Equation with a variable under radical sign Extraneous Solutions: Extra solutions that do not satisfy original equation because of the.

4.3 Notes : Solving Radical Equations A radical equation is an equation that contains a variable under a radical symbol The parent radical function is.

7.5a Solving Radical Equations. Radical Equations To solve a radical equation 1.Isolate the radical completely 2.Raise both sides to the power of the.

You can solve some absolute-value equations using mental math. For instance, you learned that the equation | x |  8 has two solutions: 8 and  8. S OLVING.

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.

11.3 Solving Radical Equations Definitions & Rules Simplifying Radicals Practice Problems.

Solving Radical Equations Steps Examples. Solving an Equation Containing a Radical  Steps  Isolate the radical  Take BOTH sides to the power.

SOLVING RADICAL EQUATIONS WITH EXTRANEOUS SOLUTIONS Unit 2E Day 5.

Vocabulary Square Root: If A = s 2, then s is a ____________________ of A. example: 25 = 5 2, 5 is a square root of 25 Cube Root: If V = s 3, then s is.

Aim #1.6: How do we solve other types of equations?

5.8 Radical Equations and Inequalities

7.6 Solving Radical Equations

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,

Solve Radical Equations

Objective Solve radical equations..

6.5 Solving Radical Equations & Inequalities

Solving Equations Containing

Solving Equations Containing

Warm-up 1. Answer: 3, Answer: 5 3. Answer: 8.

Math 71B 7.6 – Radical Equations.

Getting the radical by itself on one side of the equation.

Solving Radical Equations

Solving Equations Containing

Squaring a value and finding its square root is the opposite

Solving Square Root Equations

SECTION 10-4 : RADICAL EQUATIONS

Solving Radical Equations

Solving a Radical Equation

6-7: Solving Radical Equations

Exercise Solve x – 14 = 35. x = 49.

Solving Absolute Value and Radical Equations

7.6 Solving Radical Equations

Warm UP Simplify .

6.6 Solve Radical Equations

Section 5.8 Solving Radical Equations

Solving Equations Containing

Equations Involving Absolute Value

Presentation transcript:

S OLVING R ADICAL E QUATIONS Objective: solve simple radical equations and check for extraneous solutions How do you undo a square root or a cube root?

V OCABULARY Radical Symbol

Square Root Ex. 9 = 3 ∙ 3 Cube Root Ex. 8 = 2 ∙ 2 ∙ 2 Fourth Root etc.

R ATIONAL (F RACTION ) E XPONENTS

R E - WRITE EACH IN RADICAL FORM :

R EMEMBER … A square root “undoes” a square A cube root “undoes” a cube

T HEREFORE … A square “undoes” a square root A cube “undoes” a cube root

H OW TO SOLVE A RADICAL EQUATION Step 1: Step 1: Put in radical form if necessary Step 2: Step 2: Get radical symbol alone Step 3: Step 3: Square or cube both sides Step 4: Step 4: Drop the radical symbol Step 5: Step 5: Solve Step 6: Step 6: Check your answers!! *Might be extraneous

E X 1) S OLVE FOR X

E X 2) S OLVE FOR X

E X 3) S OLVE FOR X

E X 4) S OLVE FOR X

S OLVE & C HECK S OLUTIONS x = 17

S OLVE & C HECK S OLUTIONS x = 6

S OLVE & C HECK S OLUTIONS x = 64

S OLVE & C HECK S OLUTIONS x = -1

S OLVE & C HECK S OLUTIONS x = 59

S OLVE & C HECK S OLUTIONS x = 727

S OLVE & C HECK S OLUTIONS x = 1 x = 4

S OLVE & C HECK S OLUTIONS x = -2 extraneous x = 1

S OLVE & C HECK S OLUTIONS No Solution