Square Root vocab. And Square Root Notes absent copy Monday 5/5

Slides:

Advertisements

Similar presentations

Cubed Roots, Add/sub Sq. Roots and non-square integers notes Absent notes Tues/Wed 5/6,7.

Advertisements

Introduction to Radicals

Aim: How do we simplify radical expressions? Do Now: List at least 3 factors of: x 4.

Section 7.1 Basic of Roots (Radicals). Definition of a Square Root if and only if is a square root of.

Introduction to Radicals If b 2 = a, then b is a square root of a. MeaningPositive Square Root Negative Square Root The positive and negative square.

1 Topic Square Roots. 2 Topic Square Roots California Standard: 2.0: Students understand and use such operations as taking the opposite, finding.

SIMPLIFYING SQUARE ROOTS. Definition of radicals Square roots usually show up in radical signs. “Radical” is another word for root: The square root of.

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.

Warm Up Simplify using only positive exponents. 1.7n 2 3n 5 2.(4y 6 ) 3 Solve for the value of x. 3.

7.1 – Radicals Radical Expressions

Chapter 8 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Slide Copyright © 2009 Pearson Education, Inc. 5.4 The Irrational Numbers and the Real Number System.

Ch 9: Quadratic Equations B) Square Roots Objective: To solve quadratic equations using square roots.

Inverse operations w/equations using exponents and square roots notes Absent copy Friday 5/9.

Find the area of each square. How do you find the area of each square? Area may be found by either counting the number of units or multiply length of.

SIMPLIFYING RADICALS. Definition of radicals “Radical” is another word for root: Square root cube root fourth root, etc.

R a d i c a l U n i t Square Roots of Prefect Squares Medina1.

Objective: Add, subtract and multiplying radical expressions; re-write rational exponents in radical form. Essential Question: What rules apply for adding,

Roots and Radicals. Radicals (also called roots) are directly related to exponents.

R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.

You should know or start to recognize these: 2 2 = 43 2 = 94 2 = = = 83 3 = = = = = = = = 323.

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.

7-1 R OOTS AND R ADICAL E XPRESSIONS Finding roots and simplifying radical expressions.

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

Roots of Real Numbers.

Chapter 8 Section 1. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Evaluating Roots Find square roots. Decide whether a given root.

Radicals Tammy Wallace Varina High. Perfect Squares A number is a perfect square if it is the product of a number and itself. The first 12 perfect squares:

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)

5-5 Roots of Real Numbers Objective: Students will be able to simplify radicals.

Simplifying Radical Expressions

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

3.2 Apply Properties of Rational Exponents Do properties of exponents work for roots? What form must they be in? How do you know when a radical is in simplest.

Solving Radical Equations Chapter 7.6. What is a Radical Equation? A Radical Equation is an equation that has a variable in a radicand or has a variable.

Warm-up Write as a rational exponent. Answers:. Notes P3, Day 3: Cube Roots and Rational Exponents Definition of the Principal nth Root of a Real Number.

Square Roots Unit 1D Day 17. Do Now What are the factors of x ² + 2 x – 3? Solve for x : x ² + 2 x – 3 = 0 What are the x -intercepts of y = x ² + 2 x.

The exponent is most often used in the power of monomials.

P. 3 Radicals and Rational Exponents Q: What is a radical

By, Mrs. Muller. This is the Radical Sign 3 This is the Index: When there is no number, it is a 2 4 This is the Radicand.

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.

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

Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.

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.

Chapter 8 Section 1.

7.1 – Radicals Radical Expressions

Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. radical sign index radicand This symbol is the.

Simplifying Radical Expressions (10-2)

11.1 and 11.2 Radicals List all the perfect squares:

Honors Algebra II with Trigonometry

6.5 Solving Radical Equations & Inequalities

Rational and Irrational Square Roots

Properties and Rules for Exponents Properties and Rules for Radicals

The Radical Square Root

3-8 Solving Radical equations

Unit 3B Radical Expressions and Rational Exponents

Radicals Radical Expressions

The Irrational Numbers and the Real Number System

7. Roots and Radical Expressions

Square Roots of Perfect Squares

Radicals and Radical Functions

Introduction to Radicals Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical.

Simplifying and Rationalizing

7.1 – Radicals Radical Expressions

Section 7.1 Radical Expressions

Honors Algebra II with Trigonometry Mr. Agnew

Radicals and Radical Functions

Pre-Algebra Roots and Radicals.

Warm Up Simplify 1)

7.1 – Radicals Radical Expressions

Presentation transcript:

Square Root vocab. And Square Root Notes absent copy Monday 5/5

Index Radical = Grouping Symbol Radicand = Term inside A Root is one of the factors of the radicand. What are two of the same roots (factors) that equals 9 (radicand) when you multiply? 3 · 3 =9 Or -3 · -3 =9 factor factor factor factor You can write the root as ± 3 Principal root is always the Positive root (factor) What is the principal root of 9? 3 Index tells you how many of the same factors equals the radicand. Ex: 1 How many factors do we need to multiply to get the radicand? 4 · 4 or -4 · -4 ± 4 Ex: 2 How many factors do we need to multiply to get the radicand? 2 · 2 · 2 · 2 ±2

Variables always have a positive root because you don’t know if the variable represents a pos. or neg. #. Ex: 2 = h · h so the answer is h Exponent rule: When bases are the same and you are multiplying you add the exponents. Ex: b2 · b2 = b2 + 2 = b4 When exponents are inside the radical sign find the same 2 factors of the exponent so when you add them they equal the exponent. Ex: 8 = d4 · d4 = d4 + 4 = d8 factor factor

Example 1 15 Find the two square roots. 15 · 15 factor factor 15 · 15 factor factor -15 · -15 factor factor What is the radicand? A radicand is the term inside of the radical sign. 225 What 2 factors (the same) can we multiply to equal the radicand? (Hint there are 2 sets of factors) The 2 same factors are 15 and 15 or -15 and -15. What is the best way to write down the solution? The best way to write down the solution is to write it like: ± 15 15

Example 2 11d7 What is the principal root of this expression? 14 exponent rule = d7 • d7 = d7 + 7= d14 11d7 · 11d7 factor factor Solution What is the radicand? The radicand is 121d14 What is the index and what does it mean? 2 The index tell us how many factors = the radicand. 2 factors What is the exponent rule we can use to factor the 14? When bases are the same and we are multiplying we can add the exponents. What 2 factors (the same) can we multiply to equal the radicand? 11d7 · 11d7 What does principal root mean? Principal root is always the positive factor. 11d7

Example 3 Side = 9 ft (hint s = ) 9 • 9 9 ft factor factor 9 ft If the flag of Switzerland has an area of 81 ft2, what is the length of each of its sides? The flag is square. (hint s = ) 9 • 9 9 ft factor factor 9 ft Solution What is the radicand? The radicand is the area of the flag which is 81. Do we only find the principal root? YES or NO You can only have positive lengths. What 2 factors (the same) can we multiply to equal the radicand? The 2 factor that make up 81 are 9 and 9. What is the length of each side? The length of each side is 9 ft. flag Side = 9 ft