SIMPLIFYING RADICAL EXPRESSIONS

Slides:

Advertisements

Similar presentations

Simplify Radical Expressions

Advertisements

Warm Up Simplify each expression

Simplifying Radical Expressions Product Property of Radicals For any numbers a and b where and,

Simplifying Radicals. Perfect Squares Perfect Cubes

1-3 Square Roots Warm Up Lesson Presentation Lesson Quiz

Dividing Radicals Note- Notes for rationalizing denominators are included in this powerpoint, yet students are not required to rationalize radical denominators.

Binomial Radical Expressions

Simplifying Radical Expressions

Identify the perfect square in each set , 81, 27, , 99, 8, , 84, 12, , 216, 196, 72 Find the Prime Factorization of.

5.5 Roots of Real Numbers and Radical Expressions.

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

 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.

Rationalizing the Denominator. Essential Question How do I get a radical out of the denominator of a fraction?

Simplifying Radical Expressions Chapter 10 Section 1 Kalie Stallard.

Objectives The student will be able to: 1. simplify square roots, and 2. simplify radical expressions.

Lesson 10-3 Warm-Up.

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

Simplifying Radicals Section 5.3. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator.

Including Rationalizing The Denominators. Warm Up Simplify each expression

6.3 Binomial Radical Expressions P You can only use this property if the indexes AND the radicands are the same. This is just combining like terms.

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

Simplifying Radicals. Perfect Squares

Multiplying and Dividing Radicals The product and quotient properties of square roots can be used to multiply and divide radicals, because: and. Example.

Copyright © Cengage Learning. All rights reserved. Roots, Radical Expressions, and Radical Equations 8.

5.4 Irrational Numbers. Irrational numbers Irrational numbers are those that cannot be written as a fraction Irrational numbers have non-terminating or.

Chapter 9 Section 4 Dividing Square Roots. Learning Objective 1.Understand what it means for a square root to be simplified 2.Use the Quotient Rule to.

Conjugate of Denominator

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

Conjugate: Value or that is multiplied to a radical expression That clears the radical. Rationalizing: Removing a radical expression from the denominator.

Simplifying Radicals Binomial Conjugate:

Chapter 11 Sec 1 Simplifying Radical Expressions.

Radicals (Square Roots). = 11 = 4 = 5 = 10 = 12 = 6 = 7 = 8 = 9 = 2.

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.

Holt Algebra Multiplying and Dividing Radical Expressions Warm Up Simplify each expression

3.4 Simplify Radical Expressions

 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.

Rationalizing Numerators and Denominators of Radical Expressions Rationalize denominators. 2.Rationalize denominators that have a sum or difference.

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

 Simplify then perform the operations indicated….

Solve Quadratic Equations by Finding Square Roots Chapter 1.5.

Warm Up Simplify each expression

Multiplying and Dividing Radial Expressions 11-8

Roots, Radicals, and Root Functions

Multiplying and Dividing Radial Expressions 11-8

Multiplying and Dividing Radical Expressions

6.2 Multiplying and Dividing Radical Expressions

Unit #2 Radicals.

Multiplying Radicals.

Simplifying Radical Expressions

Do-Now: Simplify (using calculator)

Simplifying Radicals.

Simplifying Radical Expressions

Multiplying and Dividing Radial Expressions 11-8

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

Simplifying Radical Expressions

Warm up Simplify

Simplifying Radical Expressions

Simplifying Radical Expressions

Warm Up Simplify each expression

Simplify Radical Expressions

Properties of Radicals

5.2 Properties of Rational Exponents and Radicals

1.2 Multiply and Divide Radicals

Warm Up Simplify 1)

Simplifying Radicals.

Simplifying Radical Expressions

Chapter 8 Section 4.

Dividing Radical Expressions

Simplifying Radical Expressions

Presentation transcript:

SIMPLIFYING RADICAL EXPRESSIONS A RADICAL EXPRESSION is an expression that contains a square root. Examples: or The RADICAND is the expression under the radical sign. For , the radicand is 5ab3

SIMPLIFYING RADICAL EXPRESSIONS A radical expression is in SIMPLEST FORM if it contains no perfect square factors other than 1. Examples: is in simplest form. is NOT in simplest form. Why?

FLASH CARDS Simplified or Not? YES! J

FLASH CARDS Simplified or Not? NO! 4 is a factor! L

FLASH CARDS Simplified or Not? NO! x2 is a factor! L

FLASH CARDS Simplified or Not? NO! 9x2 is a factor! L

FLASH CARDS Simplified or Not? YES! J

SIMPLIFYING RADICAL EXPRESSIONS PRODUCT PROPERTY OF SQUARE ROOTS

SIMPLIFYING RADICAL EXPRESSIONS SIMPLIFYING RADICALS

SIMPLIFYING RADICAL EXPRESSIONS SIMPLIFYING RADICALS NOTICE THAT ONLY THE POSITIVE SQUARE ROOT IS USED.

FLASH CARDS Simplify J

FLASH CARDS Simplify J

FLASH CARDS Simplify J

FLASH CARDS Simplify J

FLASH CARDS Simplify J

FLASH CARDS Simplify J

SIMPLIFYING RADICAL EXPRESSIONS are examples of irrational numbers. Simplified expressions can not have irrational numbers (square roots) in their denominators. RATIONALIZING THE DENOMINATOR is a method used to eliminate radicals from the denominator of a fraction.

SIMPLIFYING RADICAL EXPRESSIONS Step 1: Multiply numerator & denominator by the radical in the denominator. Step 2: Simplify, Reduce

SIMPLIFYING RADICAL EXPRESSIONS Step 1: Multiply numerator & denominator by the radical in the denominator.

SIMPLIFYING RADICAL EXPRESSIONS Can we just divide? Simplify: YES! Step 1: Multiply numerator & denominator by the radical in the denominator. Step 2: Simplify, Reduce

SIMPLIFYING RADICAL EXPRESSIONS If the denominator is a binomial with a radical, i.e. Then multiply the numerator and denominator by the CONJUGATE of the denominator. The conjugate of is The conjugate of is

SIMPLIFYING RADICAL EXPRESSIONS Step 1: Multiply numerator & denominator by the conjugate of the denominator. Step 2: Simplify, Reduce

SIMPLIFYING RADICAL EXPRESSIONS Try this one: Step 1: Multiply numerator & denominator by the conjugate of the denominator. Step 2: Simplify, Reduce

SIMPLIFYING RADICAL EXPRESSIONS Try this one: Step 1: Multiply numerator & denominator by the conjugate of the denominator. Step 2: Simplify, Reduce

SIMPLIFYING RADICAL EXPRESSIONS Try this one: