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

Slides:

Advertisements

Similar presentations

Find Square Roots and Compare Real Numbers

Advertisements

(as opposed to fake numbers?)

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

Rational and Irrational Numbers

Questions from HW??? Use Square Roots to Solve Quadratic Equations Test: FRIDAY!!!!

NUMBER SYSTEMS ⅝ 25 √7 π

Sections 11.1: Square Roots & 11.2: Approximating Square Roots Pg.533, 540.

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

Vocabulary Section 1-3. Vocabulary Section 1-3 continued…

Real Numbers and the Number Line

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

1.3 – Real Numbers and the Number Line. I.SQUARES and SQUARE ROOTS: The term square root comes from the AREAS of squares and their sides. Because 9 =

Identify and describe patterns by explaining its properties.

Goal 1.01 Vocabulary  H J MacDonald Middle  8 th Grade Math  Littleton.

Holt Algebra Square Roots and Real Numbers 1-5 Square Roots and Real Numbers Holt Algebra 1 Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

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

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.

Algebra 1 Chapter 1 Section 5.

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

1 -2 Properties of Real Numbers. Types of Numbers  Often, numbers are grouped or classified as specific types of numbers. We will explore the following.

REAL NUMBERS (as opposed to fake numbers?) Two Kinds of Real Numbers Rational Numbers Irrational Numbers.

Rational and Irrational Numbers. Standards: Use properties of rational and irrational numbers.  MGSE9–12.N.RN.2 Rewrite expressions involving radicals.

Warm Up - Copy the following vocabulary words 1. Index: The number outside the radical symbol. 2. Radicand: is the number found inside a radical symbol,

9.1 To evaluate square roots Objective Part I Evaluating Square Roots

1-3 REAL NUMBERS AND THE NUMBER LINE I Can: - classify, graph, and compare real numbers. - find and estimate square roots.

Not all numbers or expressions have an exact square or cube root. If a number is NOT a perfect square or cube, you might be able to simplify it. Simplifying.

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

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

Rational and Irrational Numbers

Square Roots and Real Numbers

1.3 Real Numbers: Radical Symbol (√ ): A nonnegative square root called the principal square root. Radicand: The expression under the radical symbol Square.

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,

Lesson 2-7 Square Roots and Real Numbers. Definitions: Square Root- one of two equal factors of a number. Perfect Square- A number, like 64, whose square.

Simplifying Radical Expressions

Simplified Radical Form Objective: 1)Describe simplified Radical Form 2)Simplify radical expressions by a) Factoring out perfect squares b) Combine Like.

REAL NUMBERS (as opposed to fake numbers?) Two Kinds of Real Numbers Rational Numbers Irrational Numbers.

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.

REAL NUMBERS (as opposed to fake numbers?) Two Kinds of Real Numbers Rational Numbers Irrational Numbers.

WARM-UP. REAL NUMBERS THE REAL NUMBERS FLOW CHART REAL NUMBERS RATIONAL IRRATIONAL INTEGERS WHOLE NATURAL.

9.1 – Finding Square Roots. We know how to find the square of a number: 3 2 = (-3) 2 =

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.

Warm Up Find each quotient / divided by 3/5

Numbers Free powerpoints at

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.

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

The set of real numbers consists of the set of rational numbers and the set of irrational numbers. Irrational numbersRational numbers Real Numbers Integers.

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.

Real Numbers and the Number Line

TOPIC 18.1 Radical Expressions

11.1 and 11.2 Radicals List all the perfect squares:

Standard 2.0 Three Key Terms One Rule

2.7 Square Roots and Real Numbers

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.

§5.4, Irrational Numbers.

Lesson 5 Roots Lesson 6 Estimate Roots

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

Objectives Evaluate expressions containing square roots.

0-2 Real Numbers.

Presentation transcript:

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

VOCABULARY TO KNOW  Square Root  A number a is a square root of a number b if a 2 = b  Example: 7 2 = 49, so 7 is the square root of 49.

SQUARE ROOT  You can use the definition of square root to find the exact square roots of some nonnegative numbers.  The radical symbol indicates a nonnegative square root, that is also called the principal square root.

VOCABULARY TO KNOW  Radicand  The expression under the radical symbol is called the radicand.  x is the radicand in this case

VOCABULARY TO KNOW  Radical  Together, the radical symbol and radicand form a radical.

SIMPLIFYING SQUARE ROOT EXPRESSIONS

VOCABULARY TO KNOW  Perfect Square  The square of an integer  For this class, you are required to memorize all perfect squares from  Copy this list and study it. 1 2 = 17 2 = = 48 2 = = 99 2 = = = = = = = 144

ESTIMATING A SQUARE ROOT

YOU TRY!

TYPES OF NUMBERS  Numbers can be classified by their characteristics.  Some can be represented on the number line.

SETS  Numbers are classified using sets.  Set - a well-defined collection of objects.  Each object is an element of the set.  Subset - consists of elements from the given set.

Sets of Numbers

45678 Irrational numbers cannot be written as a quotient of two integers. Square root of any non-perfect square is irrational Decimals are non-terminating Ex: …, … 3

REAL NUMBERS  Rational numbers and irrational numbers form the set of real numbers.  Subsets of real numbers:  Natural  Whole  Integer  Rational  Irrational