Simplify Radicals.

Slides:

Advertisements

Similar presentations

Simplify Radical Expressions

Advertisements

Warm Up Simplify each expression

Section P3 Radicals and Rational Exponents

Examples for Rationalizing the Denominator Examples It is improper for a fraction to have a radical in its denominator. To remove the radical we “rationalize.

SQUARE ROOT METHOD. Simplify Radicals A. Single Ex.

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

Appendix:A.2 Exponents and radicals. Integer Exponents exponent base.

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

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.

Find the Square Root: 1) 3) 2) 4)

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

3.6 Solving Quadratic Equations

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

6.1 – Rational Exponents Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical.

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

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

Lesson 10-3 Warm-Up.

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.

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

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

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.

Lesson 0 – 9 Square Roots and Simplifying Radicals

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

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.

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

SIMPLIFYING RADICAL EXPRESSIONS

Fricovsky 4.5: Do Now: Simplify. 1.

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.

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

X 5√3 10.  45  33  75  28  50  27  112  180.

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.

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

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

Date: Topic: Simplifying Radicals (9.1) Warm-up:Find the square root Simplify the radical:

 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.

A or of radicals can be simplified using the following rules. 1. Simplify each in the sum. 2. Then, combine radical terms containing the same and. sumdifference.

Simplifying Radicals Algebra I Unit 1 D2. Perfect Squares

1 Objectives To simplify radical expressions To rationalize radicals in denominators To list Pythagorean triples To apply the Pythagorean Theorem in classifying.

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

Warm Up Simplify each expression

Multiplying and Dividing Radial Expressions 11-8

Roots, Radicals, and Root Functions

Simplifying Square Roots

Use Properties of Radicals to simplify radicals.

Do-Now: Simplify (using calculator)

3.4 Notes Irrational Numbers.

Simplifying Radicals.

Simplifying Radical Expressions

Multiplying and Dividing Radial Expressions 11-8

Warm up Simplify

Simplify Complex Rational Expressions

Rationalizing Roots Objective:

Complete each equation. 1. a 3 = a2 • a 2. b 7 = b6 • b

Quadratic Equations & Square Roots

Warmup Find the exact value. 1. √49 2. –√144.

Warm Up = = = = = = = =.

5.2 Properties of Rational Exponents and Radicals

Section 7.2 Rational Exponents

Warm Up Simplify 1)

10-1 Simplifying Radicals

Chapter 8 Section 4.

Unit 1.3 Part A Learning Goal:

Dividing Radical Expressions

Roots, Radicals, and Root Functions

Presentation transcript:

Simplify Radicals

Steps Test perfect squares in the calculator Make a list of perfect squares up to (if needed) Use the list to simplify non-perfect squares- go to the perfect square larger than the radical to be simplified. Make 2 new radicals, and simplify

examples

MORE EXAMPLES Simplify:

Rationalizing the denominator Steps: Multiply the numerator and denominator by the denominator and simplify

EXAMPLES Simplify:

More Examples Simplify

Square root property- no imagimary Steps: Isolate the squared term Take the square root of both sides and simplify

examples 1. 2.

examples 3. 4.

examples 5. 6.

examples 7. 8.

examples 9.