Simplifying Radicals.

Slides:

Advertisements

Similar presentations

Working With Surds.. What Is A Surd ? Calculate the following roots: = 6= 2 = 3= 5= 2 All of the above roots have exact values and are called rational.

Advertisements

Simplifying Radicals. Perfect Squares Perfect Cubes

Homework Solution lesson 8.5

The Laws Of Surds.

Square Roots Simplifying Square Roots

Binomial Radical Expressions

5-6 Radical Expressions Objectives Students will be able to: 1)Simplify radical expressions 2)Add, subtract, multiply, and divide radical expressions.

11-2: Operations with Radical Expressions

6.2 – Simplified Form for Radicals

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

Radical Operations Adding & Subtracting Radicals 1Copyright (c) 2011 by Lynda Greene Aguirre.

Adding, Subtracting, Multiplying, & Dividing Rational Expressions

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

28/07/10 SURDS What is a surd? Manipulating and simplifying surds.

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

Introduction to Complex Numbers Adding, Subtracting, Multiplying And Dividing Complex Numbers SPI Describe any number in the complex number system.

Add & Subtract Rationals – Common Denominator To add or subtract rational expressions with common denominators: 1) Add or subtract the numerators 2) Write.

Simplifying Radicals. Perfect Squares

12.2 Operations with Radical Expressions √

Simplifying Radical Expressions Basic multiplication Basic division o Rationalize the denominator.

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

Integrated Mathematics

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

SIMPLIFYING RADICAL EXPRESSIONS

Copyright © Cengage Learning. All rights reserved. 8 Radical Functions.

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.

Warm Up: 1)2). 5.2 Notes: Properties of Rational Exponents and Radicals.

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

Aims: To be to be able to classify types of numbers To be able to write a surd in its simplest form To be able to add, subtract and multiply surds SURDS.

5-6 Radical Expressions Objectives Students will be able to: 1)Simplify radical expressions 2)Add, subtract, multiply, and divide radical expressions.

Simplifying Radical Expressions Objective: Add, subtract, multiply, divide, and simplify radical expressions.

3.4 Simplify Radical Expressions

5-5 ROOTS OF REAL NUMBERS Objective: Students will be able to simplify radicals.

Rationalizing Numerators and Denominators of Radical Expressions Rationalize denominators. 2.Rationalize denominators that have a sum or difference.

Fractional Expressions Section 1.4. Objectives Simplify fractional expressions. Multiply and divide fractional expressions. Add and subtract fractional.

+ Fractions. + Part of a whole + + Numerator How many pieces The number on the top of a fraction.

Introduction to Complex Numbers Adding, Subtracting, Multiplying And Dividing Complex Numbers SPI Describe any number in the complex number system.

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

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.

Manipulation of Surds.

Radical Expressions and Rational Exponents

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.

Laws of Exponents (Warm-Up)

Multiplying, Dividing, Adding & Subtracting Radicals

3.4 Notes Irrational Numbers.

Simplifying Radicals.

Radical Operations Unit 4-3.

Warm up Simplify

Radicals Simplify, Add, Subtract, Multiply, Divide and Rationalize

Simplifying Radicals 11.2.

Warm up Simplify

§5.4, Irrational Numbers.

Simplify Radical Expressions

Decimal Approximation Decimal Approximation

12.2 Operations with Radical Expressions √

Objective The student will be able to:

Simplifying Square Roots

5.2 Properties of Rational Exponents and Radicals

Roots of numbers which cannot be expressed as whole numbers are called SURDS National 5 Maths Surds.

Operations with Radical Expressions √

The Laws Of Surds..

Millburn Academy Maths department National 5 Surds 1.

Warm Up Simplify 1)

10-1 Simplifying Radicals

Chapter 8 Section 4.

Warm-ups: Simplify the following

Dividing Radical Expressions

Presentation transcript:

Simplifying Radicals

Radicals

Simplifying Radicals Express 45 as a product using a square number Separate the product Take the square root of the perfect square

Some Common Examples

Harder Example Find a perfect square number that divides evenly into 245 by testing 4, 9, 16, 25, 49 (this works)

Addition and Subtraction You can only add or subtract “like” radicals You cannot add or subtract with

More Adding and Subtracting You must simplify all radicals before you can add or subtract

Multiplication Consider each radical as having two parts. The whole number out the front and the number under the radical sign. You multiply the outside numbers together and you multiply the numbers under the radical signs together

More Examples Note that can be simplified

Try These

Division As with multiplication, we consider the two parts of the surd separately.

Division

Important Points to Note Radicals can be separated when you have multiplication and division However Radicals cannot be separated when you have addition and subtraction

Rational Denominators Radicals are irrational. A fraction with a radical in the denominator should to be changed so that the denominator is rational. Here we are multiplying by 1 The denominator is now rational

More Rationalising Denominators Multiply by 1 in the form Simplify

Review Difference of Squares When a radical is squared, it is no longer a radical. It becomes rational. We use this and the process above to rationalise the denominators in the following examples.

More Examples Here we multiply by 5 – which is called the conjugate of 5 + Simplify

Another Example Here we multiply by the conjugate of which is Simplify

Try this one The conjugate of is Simplify See next slide

Continuing

We wish to thank our supporters: