Add _ to each side. Example 1 Solve a radical equation Solve Write original equation. 3.5 Solve Radical Equations Solution Divide each side by _.

Slides:

Advertisements

Similar presentations

Simplify Radical Expressions

Advertisements

7.5 – Rationalizing the Denominator of Radicals Expressions

Warm Up Simplify each expression

1-3 Square Roots Warm Up Lesson Presentation Lesson Quiz

Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,

Homework Solution lesson 8.5

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

Square Roots Objective I can simplify radicals I can use the square root property to solve equations.

6.2 – Simplified Form for Radicals

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

Review and Examples: 7.4 – Adding, Subtracting, Multiplying Radical Expressions.

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.

Solve a radical equation

Solve an equation with an extraneous solution

Warm Up #3 Find the exact value. 2. –√ √49 ANSWER –12 7 ANSWER

Warm-Up Exercises ANSWER ANSWER x =

5.7 Complex Numbers 12/17/2012.

How do I solve absolute value equations and inequalities?

Solve an equation with an extraneous solution

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

EXAMPLE 2 Rationalize denominators of fractions Simplify

3.6 Solving Quadratic Equations

 Multiply rational expressions.  Use the same properties to multiply and divide rational expressions as you would with numerical fractions.

Unit 2 Algebra Investigations Lesson 3: Rational and Radical Expressions Notes 3.4: Simplify Radical Expressions.

Section 9.1 Finding Roots. OBJECTIVES Find the square root of a number. A Square a radical expression. B.

243 = 81 • 3 81 is a perfect square and a factor of 243.

5.3 Solving Quadratic Equations by Finding Square Roots.

5.6.1 – Square Root Method. Recall, we solved “quadratic equations” when we set a polynomial equation equal to 0 Example. x 2 + 5x + 6 = 0.

Warm-Up Exercises Find the exact value. ANSWER – 144 ANSWER 12 – Use a calculator to approximate the value of to the nearest tenth

Simplify Radical Expressions. EQs…  How do we simplify algebraic and numeric expressions involving square root?  How do we perform operations with square.

Chapter 12 Final Exam Review. Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction)

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.

5.7 Complex Numbers 12/4/2013. Quick Review If a number doesn’t show an exponent, it is understood that the number has an exponent of 1. Ex: 8 = 8 1,

Rational Equations Section 8-6.

Holt McDougal Algebra 2 Solving Rational Equations and Inequalities Solving Rational Equations and Inequalities Holt Algebra 2Holt McDougal Algebra 2.

4.5: Do Now: Review 4.3/4.4. The area of a rectangle with length = 3x + 1 and width = 2x + 1 is 22. Write and solve an equation to find the dimension of.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Find the exact value. 1.) √49 2.) - √ Use a calculator to approximate the value of √(82/16) to the nearest tenth.

Fricovsky 4.5: Do Now: Simplify. 1.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.

Advanced Algebra Notes Section 4.5: Simplifying Radicals (A) A number r is a _____________ of a number x if. The number r is a factor that is used twice.

Essential Question: What must you do to find the solutions of a rational equation?

How do I use the imaginary unit i to write complex numbers?

3.4 Simplify Radical Expressions PRODUCT PROPERTY OF RADICALS Words The square root of a product equals the _______ of the ______ ______ of the factors.

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.

EXAMPLE 3 Use properties of radicals Use the properties of radicals to simplify the expression. a =216 3 = =6 Product property b

 A radical expression is an expression with a square root  A radicand is the expression under the square root sign  We can NEVER have a radical in the.

7.5 Operations with Radical Expressions. Review of Properties of Radicals Product Property If all parts of the radicand are positive- separate each part.

Holt Algebra Solving Rational Equations Warm Up 1. Find the LCM of x, 2x 2, and Find the LCM of p 2 – 4p and p 2 – 16. Multiply. Simplify.

Holt McDougal Algebra 2 Multiplying and Dividing Rational Expressions Multiplying and Dividing Rational Expressions Holt Algebra 2Holt McDougal Algebra.

Chapter 5 Radical Expressions and Equations

1. Add: 5 x2 – 1 + 2x x2 + 5x – 6 ANSWERS 2x2 +7x + 30

EXAMPLE 2 Rationalize denominators of fractions Simplify

Do-Now: Simplify (using calculator)

Solve a quadratic equation

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

Simplifying Radical Expressions

Solve a quadratic equation

Find the least common multiple for each pair.

Find the least common multiple for each pair.

Squaring a value and finding its square root is the opposite

Warmup Find the exact value. 1. √27 2. –√

Simplify Radicals.

Warm Up #3 Find the exact value. 2. –√ √49 ANSWER –12 7 ANSWER

Notes Over Using Radicals

6.4 Completing the Square Square Root Property

Presentation transcript:

Add ___ to each side. Example 1 Solve a radical equation Solve Write original equation. 3.5 Solve Radical Equations Solution Divide each side by ___. Square each side. Simplify. Subtract ___ from each side The solutions is ____.

3.5 Solve Radical Equations Checkpoint. Complete the following exercise.

Square each side. Example 2 Solve an equation with an extraneous solution Solve Write original equation. 3.5 Solve Radical Equations Solution Simplify. Write in standard form. Factor.

Example 2 Solve an equation with an extraneous solution Solve 3.5 Solve Radical Equations Solution CHECK Check ___ and ____ in the original equation. Because ____ does not check in the original equation, it is an __________________. extraneous solution The only solution of the equation is ___.

3.5 Solve Radical Equations Checkpoint. Solve the equation.

3.5 Solve Radical Equations Checkpoint. Solve the equation.

Square each side. Example 3 Solve an equation with radicals on both sides Solve Write original equation. 3.5 Solve Radical Equations Solution Simplify. Subtract ____ from each side. Add ___ to each side. The solution is ___. Check the solution.

3.5 Solve Radical Equations Checkpoint. Solve the equation.

3.5 Solve Radical Equations Checkpoint. Solve the equation.

3.5 Solve Radical Equations Pg. 159, 3.5 #1-32

Example 2 Multiply radicals 3.4 Simplify Radical Expressions

3.4 Simplify Radical Expressions QUOTIENT PROPERTY OF RADICALS Words The square root of a quotient equals the _______ of the ______ ______ of the numerator and denominator. quotient square roots Algebra Example

Example 3 Use the quotient property of radicals Simplify. _______ _________ of radicals. Quotient property 3.4 Simplify Radical ExpressionsSimplify. _______ _________ of radicals. Quotient property

3.4 Simplify Radical Expressions Checkpoint. Simplify the expression.

Example 4 Rationalize the denominator Multiply by. 3.4 Simplify Radical ExpressionsSimplify. Product property of radicals.

Example 4 Rationalize the denominator Multiply by 3.4 Simplify Radical ExpressionsSimplify. Multiply.

Example 5 Add and subtract radicals Factor using perfect square factor. 3.4 Simplify Radical ExpressionsSimplify. Product property of radicals. Simplify.

Example 5 Add and subtract radicals Factor using perfect square factor. 3.4 Simplify Radical ExpressionsSimplify. Product property of radicals. Simplify.

3.4 Simplify Radical Expressions Checkpoint. Simplify the expression.

3.4 Simplify Radical Expressions Pg. 154, 3.4 #1 – 27