Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index.

Slides:

Advertisements

Similar presentations

Introduction to Radicals

Advertisements

Polynomials Identify Monomials and their Degree

Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index.

MTH 092 Section 15.1 Introduction to Radicals Section 15.2 Simplifying Radicals.

Section P3 Radicals and Rational Exponents

11.1 Examples for Simplifying (EX: 1 of 4) Look for factors of 50 that are perfect square numbers. Take the square root of 25. Write it outside the radical.

Square and Cube Roots Roots and Radicals Mr. O.

7.1 – Radicals Radical Expressions

RADICAL EXPRESSIONS.

Aim: Simplifying Radicals Course: Adv. Alg. & Trig. Aim: How do I tame radicals? Simply simplify! Do Now: Find the solution set and graph the inequalities.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Tidewater Community College

11.3 Simplifying Radicals Simplifying Radical Expressions.

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

Find square roots. Find cube roots. 7.1 Objective The student will be able to:

Working with Negative Exponents When working with negative exponents, move the variable and change the exponent to positive.

P2 Exponents & Radicals. What does an exponent tell you?? Repeated Multiplication How many times you multiply the base by itself.

Finding an Inverse Function with a Table. Inverse Notation Original function Inverse function “Inverse of f(x)”

Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.

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

Properties of Rational Exponents and Radicals

Algebraic Expressions - Rules for Radicals Let’s review some concepts from Algebra 1. If you have the same index, you can rewrite division of radical expressions.

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

11.2A Simplify and Multiply Square Roots. Squaring a Number When a number is squared, it is multiplied to itself: Notice squaring any number.

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

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:

Simplifying Square Roots Simplifying Square Roots.

Simplifying Radicals. Radical Flashback Simplifying Radicals: 1.Find the greatest perfect square that goes into the radicand. 2.Take the square root of.

In order to add or subtract radicals: All radicals must be simplified. Then, you combine “like” terms. Square-root expressions with the same radicand.

Multiplying and Simplifying Radicals The Product Rule for Radicals is given by: Note that both of the radicals on the left have the same index. Throughout.

Radicals Simplify radical expressions using the properties of radicals

6.3 Simplifying Radical Expressions In this section, we assume that all variables are positive.

Complex Number System Adding, Subtracting, Multiplying and Dividing Complex Numbers Simplify powers of i.

Cubes and Cube Roots Wednesday, February 25 th. Objective The student will be able to simplify a cube root.

UNIT 4- radicals simplify a cube root and higher.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

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.

Unit 2: Exponents Review. What is on the test??? 1.Exponent Rules 2.Perfect Squares 3.Square Roots / Cube Roots 4.Estimating Non-Perfect Squares 5.Scientific.

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

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

Simplifying Radicals Algebra I Unit 1 D2. Perfect Squares

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

Sections 8.3 and 8.4 Simplifying Radicals Adding and Subtracting Radicals.

And Squares Square Roots. If a square measures 4 inches on each side, how would you find its area? 4 inches.

7.2 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.

Any questions about the practice? Page , 11, 13, 21, 25, 27, 39, 41, 53.

Roots, Radicals, and Complex Numbers

Unit 1: Radical Expressions

Unit 4: Coordinate Geometry

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.

Rules of Exponents Multiplying and powers

3.4 Notes Irrational Numbers.

Rational Exponents Simplifying Radical Expressions

Exponents & Radicals – Rules for Radicals

Radical Operations Unit 4-3.

The Radical Square Root

Perfect Squares & Square Roots

Multiplying and Dividing Powers

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

Unit 3B Radical Expressions and Rational Exponents

Roots, Radicals, and Complex Numbers

Square Roots of Perfect Squares

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.

5.2 Properties of Rational Exponents and Radicals

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

Square and Cube Roots Roots and Radicals.

Square Roots and Simplifying Radicals

Pre-Algebra Roots and Radicals.

Objective Solve radical equations.. Objective Solve radical equations.

Presentation transcript:

Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three.

Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three. For now we will work only with square roots.

Exponents & Radicals – Rules for Radicals A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three. For now we will work only with square roots. Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…

Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. Realize that table keeps going, I only went up to 12…. EXAMPLE :

Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : What number did I multiply to get 25 ?

Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : Notice there is no longer a radical over the answer…

Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : What number did I multiply to get 100 ?

Exponents & Radicals – Rules for Radicals Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares… To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12…. EXAMPLE : Notice there is no longer a radical over the answer…

Exponents & Radicals – Rules for Radicals So now we could create a square root table…

Exponents & Radicals – Rules for Radicals Some rules for radicals : 1. A number / variable, divided by its square root, equals its square root

Exponents & Radicals – Rules for Radicals Some rules for radicals : 1. A number / variable, divided by its square root, equals its square root 2. Numbers / variables under THE SAME root / index can be multiplied or divided

Exponents & Radicals – Rules for Radicals Some rules for radicals : 1. A number / variable, divided by its square root, equals its square root 2. Numbers / variables under THE SAME root / index can be multiplied or divided This rule also works in the OTHER direction, and is sometimes used to help simplify radicals…

Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same.

Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same. Just like

Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same. Just like

Exponents & Radicals – Rules for Radicals Some rules for radicals : 3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same. Just like You CAN NOT combine these. The number under the root is NOT the same…

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : Simplify

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20 2 nd – find the pair that has the biggest perfect square

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20 2 nd – find the pair that has the biggest perfect square 3 rd - break up your original number into this pair under radicals

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 1 : SimplifyFactors of 20 Method # 1 : 1 st – list the factors of 20 2 nd – find the pair that has the biggest perfect square 3 rd – break up the original number into that pair under radicals 4 th – simplify the square root of the perfect square

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1…

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… When your answer falls below 2 stop.

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… When your answer falls below 2 stop. Even though there are two that work, we want the LARGEST perfect square…

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… Break up your number into the perfect square that worked and the result…

Exponents & Radicals – Rules for Radicals Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part. EXAMPLE # 2 : Simplify Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder. We never use 1… Reduce your perfect square…