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

Slides:

Advertisements

Similar presentations

Simplifying, Multiplying, & Rationalizing Radicals

Advertisements

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

Simplifying Radicals you solve them? Topic: Radical Expressions

Section P3 Radicals and Rational Exponents

9.3 Simplifying Radicals.

12.5 Simplifying Square Roots CORD Math Mrs. Spitz Spring 2007.

Objectives The student will be able to:

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

Simplifying Radicals.

Binomial Radical Expressions

Simplifying When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals.

Find square roots. Find cube roots. 7.1 Objective The student will be able to:

Objectives The student will be able to: 1. simplify square roots, and 2. simplify radical expressions. SOL: A.3 Designed by Skip Tyler, Varina High School.

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

9.2 Students will be able to use properties of radicals to simplify radicals. Warm-Up  Practice Page 507 – 508 l 41, 42, 45, 46, 55, 57, 59, 65.

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.

Simplifying When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals.

Bell Ringer Use the Pythagorean Theorem to find the length of the hypotenuse.

10/29/12 Unit 2Triangles Right Triangles I can….. simplify radical expressions.

Lesson 10-3 Warm-Up.

Objectives The student will be able to: 1. simplify square roots, and 2.simplify radical expressions. Designed by Skip Tyler, Varina High School.

Introduction to Irrational Numbers We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.” √ 3 is an irrational.

Bell Ringer Use the Pythagorean Theorem to find the length of the hypotenuse.

11-4 Multiplying and Dividing Radical Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

CONFIDENTIAL 1 Algebra1 Multiplying and Dividing Radical Expressions.

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.

SWBAT…simplify radicals using the product property of radicalsWed, 3/14 Agenda 1. WU (10 min) 2. Lesson on product property of radicals – 13 examples!

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

11-1 Simplifying Radicals

SIMPLIFYING RADICAL EXPRESSIONS

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

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

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

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

Simplifying Radicals Algebra I Unit 1 D2. Perfect Squares

Simplify – No negative exponents. Binomial Radical Expressions I can add and subtract radical expressions.

Chapter R Section 7: Radical Notation and Rational Exponents

Radicals. Parts of a Radical Radical Symbol: the symbol √ or indicating extraction of a root of the quantity that follows it Radicand: the quantity under.

Warm Up Simplify each expression

Multiplying and Dividing Radial Expressions 11-8

Roots, Radicals, and Root Functions

Multiplying and Dividing Radial Expressions 11-8

1.6 Objectives The student will be able to:

Warm-Up: HW #5: Simplifying radicals Agenda WU (10 min)

Multiplying Radicals.

Simplifying Radical Expressions

Objectives The student will be able to:

Do-Now: Simplify (using calculator)

Simplifying Radical Expressions

Objectives The student will be able to:

Simplifying Radical Expressions

Objectives The student will be able to:

Dividing Radical Expressions.

Simplifying Radical Expressions

Simplifying Radical Expressions

Warm Up Simplify each expression

If x2 = y then x is a square root of y.

5.2 Properties of Rational Exponents and Radicals

Objectives The student will be able to:

Objectives The student will be able to:

Objectives The student will be able to:

9.3 Simplifying Radicals. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a.

Simplifying Radical Expressions

Objectives The student will be able to:

Dividing Radical Expressions

Simplifying Radical Expressions

Objectives The student will be able to:

Objectives The student will be able to:

Section 9.1 “Properties of Radicals”

Presentation transcript:

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

In the expression, is the radical sign and 64 is the radicand. If x 2 = y then x is a square root of y. 1. Find the square root: 8 2. Find the square root: -0.2

11, Find the square root: 21 5.Find the square root: 3. Find the square root:

6.82, Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.

1 1 = = = = = = 36 49, 64, 81, 100, 121, 144,... What numbers are perfect squares?

1. Simplify Find a perfect square that goes into 147.

2. Simplify Find a perfect square that goes into 605.

Simplify

Look at these examples and try to find the pattern… How do you simplify variables in the radical? What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

Find a perfect square that goes into Simplify 5. Simplify

Simplify 1.3x 6 2.3x x 6 4.9x 18

Multiply the radicals. 6. Simplify

7. Simplify Multiply the coefficients and radicals.

Simplify

How do you know when a radical problem is done? 1.No radicals can be simplified. Example: 2.There are no fractions in the radical. Example: 3.There are no radicals in the denominator. Example:

8. Simplify. Divide the radicals. Uh oh… There is a radical in the denominator! Whew! It simplified!

9. Simplify Uh oh… Another radical in the denominator! Whew! It simplified again! I hope they all are like this!

10. Simplify Since the fraction doesn’t reduce, split the radical up. Uh oh… There is a fraction in the radical! How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!

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

Product Property of Radicals Examples

Examples:

Quotient Property of Radicals For any numbers a and b where and,

Examples:

Simplest Radical Form No perfect nth power factors other than 1. No fractions in the radicand. No radicals in the denominator.

Adding radicals We can only combine terms with radicals if we have like radicals Reverse of the Distributive Property

Examples:

Multiplying radicals - Distributive Property

Multiplying radicals - FOIL F O I L

Examples: F O I L

F O I L

Conjugates Binomials of the form where a, b, c, d are rational numbers.

The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

Examples: