Simplifying Radical Expressions

Slides:

Advertisements

Similar presentations

Simplify Radical Expressions

Advertisements

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

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

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.

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

Solve an equation with an extraneous solution

Section 7.6 Solving Radical Equations  The Power Principle for Equations If A = B then A n = B n  The Danger in Solving an Equivalent Equation  Equations.

Other Types of Equations

Algebra 2 Bellwork – 3/4/15.

Tidewater Community College

Solve an equation with an extraneous solution

EXAMPLE 2 Rationalize denominators of fractions Simplify

WARM UP POWER OF A PRODUCT Simplify the expression. 1.(3x) 4 2.(-5x) 3 3.(xy) 6 4.(8xy) 2 4.

2.13 Warm Up x² - 2x + 15 = 0; 3 x² + 3x – 4 = 0; 1

3.6 Solving Quadratic Equations

Simplifying Radical Expressions Chapter 10 Section 1 Kalie Stallard.

Algebra 2: Unit 8 Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.

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

Goal: Solving quadratic equations by finding square roots.

Chapter 1 - Fundamentals Equations. Definitions Equation An equation is a statement that two mathematical statements are equal. Solutions The values.

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)

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

Chapter 10.5 Notes Part I: Simplify Radical Expressions Goal: You will simplify radical expressions.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions.

Simplify Radical Expressions Warm-up: Recall how to estimate the square root of a number that is not a perfect square. 1.) The is between the perfect square.

7.5 Warm-Up Solve. 1. x5/2 = x2/ = 24 x2/3 = 9

Topic 4 Real Numbers Rational Numbers To express a fraction as a decimal, divide the numerator by the denominator.

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

Solving Radical Inequalities. Solving radical inequalities is similar to solving rational equations, but there is one extra step since we must make sure.

Exponents and Radicals

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

Warm-Up Find the inverse: 1.3y = 12x f(x) = ½x + 8.

5-8 RADICAL EQUATIONS & INEQUALITIES Objectives Students will be able to: 1) Solve equations containing radicals 2) Solve inequalities containing radicals.

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

Standard 8 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x.

5-8 Radical Equations and Inequalities Objectives Students will be able to: 1)Solve equations containing radicals 2)Solve inequalities containing radicals.

Copyright © Cengage Learning. All rights reserved. Fundamentals.

LESSON 12.1 OBJECTIVE: IDENTIFY OR ESTIMATE SQUARE ROOTS, DEFINE AND WRITE SQUARE ROOTS IN SIMPLEST RADICAL FORM. Simplifying Radicals.

1.2 Quadratic Equations. Quadratic Equation A quadratic equation is an equation equivalent to one of the form ax² + bx + c = 0 where a, b, and c are real.

Quadratic Equation U n i t Solving by taking the Square Root Medina 1.

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

Chapter 5 Radical Expressions and Equations

Section 2.6 – Other Types of Equations

Quadratic Equation Unit

Algebra 1 Section 9.2 Simplify radical expressions

6.2 Multiplying and Dividing Radical Expressions

Simplifying Radical Expressions

EXAMPLE 2 Rationalize denominators of fractions Simplify

Do-Now: Simplify (using calculator)

Simplifying Radical Expressions

12.1 Operations with Radicals

4 WARM UP SCIENTIFIC NOTATION Write the number in scientific notation.

Solving Equations Containing

3-8 Solving Radical equations

Solving Radical Equations

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Solving Equations Containing

Solving Equations Containing

Notes Over 9.2 Simplest Form of Radicals

5.2 Properties of Rational Exponents and Radicals

SECTION 10-4 : RADICAL EQUATIONS

Solving Square Root and Other Radical Equations

Aim: How do we solve radical equations?

GSE Algebra I Today’s Question: How do we simplify square roots?

Solve Quadratic Equations by Finding Square Roots Lesson 1.5

Section 9.1 “Properties of Radicals”

Solving Equations Containing

Solving Square Root and Other Radical Equations

Presentation transcript:

Simplifying Radical Expressions

How to solve the problem Simplifying Radical Expressions How to solve the problem Steps 1. Isolate the radical on One side of the equation 2.Square each side to eliminate The radical -simplify -set equal to zero 3.Check your answer 3+Square root of m =13 Example 3+m =13 -3 -3 m =10  m²=(10)² m=100 3+ 100 =13 3+10=13 13=13

Professions Racing Physics

Explanation Of Your Topic (What you will learn from simplifying radical expressions.) To simplify square roots To simplify radical expressions Simplifying radical expressions are Equations that contain radicals With variables in the radicand. Simplest Radical Form: A radical expression is in the simplest radical form when the following three conditions have been met. No radicands have perfect square factors other then one No radicands contain fractions No radicals appear in the denominator of the fraction.

Why is it Important to Algebra? Simplifying Radical Expressions are important to algebra because you can use radical expressions to solve problems involving physics and racing.

Real Life Example (Oceanography) The Tonga Trench in the Pacific Ocean is a Potential Source for a Tsunami, a large ocean wave generated by an undersea earthquake. The Formula for a Tsunami’s speed s in meters per second is s = 3.1d, where d is the depth of the ocean in meters. Equations like s = 3.1 d that contain radicals with Variables in the radicand are called radical equations. To solve these Equations, first isolate the radical on one side of the equation. Then square Each side of the equation to eliminate the radical. Find the depth of the Tonga Trench if a Tsunami’s speed is 322 Meters per second.

Real Life Example (Oceanography) 322 = 3.1 d Replaces s with 322 322 = 3.1 d Divide each side by 3.1 3.1 3.1 (322)² = (d)² Square each side of the 3.1 equation (322)² = d Use a Scientific Calculator 3.1 to simplify (322)² 3.1 Enter: ( 322 divided by 3.1 ) x² = 10789.17794 The depth of the Tonga Trench is approximately 10,789 meters. Check this result by substituting 10,789 for d into the original Formula.

THAT’S ALL FOLKS By Melinda and Emma