11.1 and 11.2 Radicals List all the perfect squares:

Slides:

Advertisements

Similar presentations

Find Square Roots and Compare Real Numbers

Advertisements

Real Numbers and The Number Line

R a d i c a l U n i t Rationalizing the Denominator Medina1.

Squares and Square Roots Objective: Students will be able to successfully multiply and simplify expressions using squares and square roots. Warm-Up Evaluate:

Squares and Square Roots Objective: Students will be able to successfully multiply and simplify expressions using squares and square roots. Warm-Up Evaluate:

11.1 and 11.2 Radicals Goal(s): 1.To find the square roots of perfect squares, perfect square radicands and estimate the roots of irrational numbers 2.Determine.

Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.

Warm Up Simplify each expression. 1. 6²

Simplifying Radicals.

Mrs.Volynskaya Real Numbers

11-2 Radical Expressions Standard 2.0 Three Key Terms One Rule.

Real Numbers Real Numbers are all numbers that can be located on Real Number line. This includes all whole numbers, all fractions, all decimals, all roots,

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 5 Number Theory and the Real Number System.

Evaluating Square Roots

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

VOCABULARY. The set {0, 1, 2,….} Whole Numbers VOCABULARY Lines and sets that never end continue to… Infinity.

9.1 To evaluate square roots Objective Part I Evaluating Square Roots

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

Goal: Solving quadratic equations by finding square roots.

Rational Square Roots Lesson x 2 = 4 3 x 3 =

Warm-Up Change each decimal to a fraction:

Section 2-8 Definitions Square root: = 6. Radical sign: This is a radical sign. Perfect square: 4, 9, 16, 25, … are perfect square numbers. Because 2*2=4,

Chapter 4 Powers and Roots. Real Numbers Rational Review Natural Numbers Whole Numbers Integers Fractions Repeating or Terminating Decimals New Perfect.

Simplifying Radical Expressions

Simplifying Radicals Square roots/perfect squares Combining Radicals Vocabulary Rationalizing Denominators Math Jeopardy.

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

Review for Unit 2 Quiz 1. Review for U2 Quiz 1 Solve. We will check them together. I will answer questions when we check answers. Combine like terms.

Radical Expressions and Functions Find the n th root of a number. 2.Approximate roots using a calculator. 3.Simplify radical expressions. 4.Evaluate.

Do Now 9/23/ A= 16 A = 4² A= 36 A = 6² 4 What is the area for each figure? What are the dimensions for each figure? Write an equation for area of.

Perfect squares: 1, 4, 9, __, __, __, __, __, __, __,…

Warm Up Find each quotient / divided by 3/5

7.1 Radicals and Radical Functions. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a.

1-2 IRRATIONAL NUMBERS AND SQUARE ROOTS I Can: - Classify numbers as rational or irrational and find and estimate square roots.

Aim: How Do We Simplify Radicals? . The entire expression, including the radical sign and radicand, is called the radical expression. radicand. 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.

Section 5-4 The Irrational Numbers Objectives: Define irrational numbers Simplify radicals Add, subtract, multiply, and divide square roots Rationalize.

Solve Quadratic Equations by Finding Square Roots Chapter 1.5.

Martin-Gay, Developmental Mathematics 1 Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of.

Simplifying Expressions with Rational Exponents and Radicals

TOPIC 18.1 Radical Expressions

Simplifying Radical Expressions (10-2)

Honors Algebra II with Trigonometry

Introduction to Radicals

Standard 2.0 Three Key Terms One Rule

2.7 Square Roots and Real Numbers

Warm Up 1.) List all of the perfect squares up to The first three are done below. 1, 4, 9,… Using a calculator, evaluate which expressions are.

The Radical Square Root

Roots of Real Numbers and Radical Expressions

All numbers that can be represented on a number line are called real numbers and can be classified according to their characteristics.

UNIT 1 VOCABULARY The Real number system.

The Irrational Numbers and the Real Number System

7. Roots and Radical Expressions

§5.4, Irrational Numbers.

Objectives Rewrite radical expressions by using rational exponents.

Roots of Real Numbers and Radical Expressions

The number inside the radical symbol

8.1 Introduction to Radicals

10.5 Use Square Roots to Solve Quadratic Equations

The Real Number System Real Numbers Irrational Numbers

Warm-Up #12 (Monday, 9/28) 3 ∙ ∙ (2 5 − 125)

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.

0-2 Real Numbers.

Section 7.1 Radical Expressions

Natural Numbers The first counting numbers Does NOT include zero

Bell Work Write each of the following as a decimal or a fraction….

Bell Work Write each of the following as a decimal or a fraction….

Do Now 4/29/19 Take out CW/HW from last week. Practice worksheet 9.1

Presentation transcript:

11.1 and 11.2 Radicals List all the perfect squares:

Square Roots Symbol: or Every positive number has both positive and negative square roots. Principal: just the positive answer Radical Sign “Principal” Square Root is the positive 5.

Simplify: Because (9)2 = 81 9 ±8 Not possible (6)2  -36 (-6)2  -36

Rational Numbers Whole #, fraction, decimal that ends or repeats, square root that is a perfect square

Irrational Numbers Square roots that are not perfect squares Decimal never ends and does not repeat. Examples of irrational numbers: 

Identify the number as irrational or rational

Identify the rational number:

Real Numbers: All the rational and all the Irrational numbers.

Radical Expressions (an expression written under a radical) Radicand (the expression written under the radical) The radicand must be positive!

If there is a variable in the radicand: and solve for the variable to find the values of x that make the expression a real number.

Determine the values of x that make the expression a real number.

Determine the values of x that make the expression a real number.

Perfect Square Radicands Rule: If the radicand contains a variable the square root needs to be in absolute values

Explanation

Simplify:

Simplify:

Simplify:

Simplify:

Homework worksheet