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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 positive integers n, if b^n = a, then b is the nth root of a.
Notation index radical radicand Note: An index of 2 is understood but not written in a square root sign.
Simplify To simplify means to find x in the equation: x 4 = 81 Solution: = 3
Principal Root The nonnegative root of a number Principal square root Opposite of principal square root Both square roots
Summary of Roots even odd one + root one - root one + root no - roots no real roots no + roots one - root one real root, 0
Rational Exponents In other words, exponents that are fractions.
Definition of For any real number a and any integer n > 1, except when a < 0 and n is even
Definition of Rational Exponents For any nonzero number b and any integers m and n with n > 1, except when b < 0 and n is even
NOTE: There are 3 different ways to write a rational exponent
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.
Monday, April 28, 2014Algebra 2 GT Objective: We will explore and define ways to simplify radical expressions. Warm Up: Rewrite each as an exponential.
Homework: pages , 29, 35, 43, 47, 49, odd, odd, 75, 79, odd.
SIMPLIFYING SQUARE ROOTS. Definition of radicals Square roots usually show up in radical signs. “Radical” is another word for root: The square root of.
5.7 Rational Exponents Fraction Exponents.
6.1 n th Roots and Rational Exponents What you should learn: Goal1 Goal2 Evaluate nth roots of real numbers using both radical notation and rational exponent.
6-3: Rational Exponents Unit 6: Rational /Radical Equations.
Warm up 1. Change into Scientific Notation 3,670,900,000 Use 3 significant figures 2. Compute: (6 x 10 2 ) x (4 x ) 3. Compute: (2 x 10 7 ) / (8.
Checking Factoring The checking of factoring can be done with the calculator. Graph the following expressions: 1.x 2 + 5x – 6 2.(x – 3)(x – 2) 3.(x.
1 7.1 and 7.2 Roots and Radical Expressions and Multiplying and Dividing Radical Expressions.
Exponents and Radicals Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Repeated multiplication can be written in.
5.5 Roots of Real Numbers and Radical Expressions.
7.1 Radical Expressions.
Copyright © 2012 Pearson Education, Inc.
§ 7.2 Radical Expressions and Functions. Tobey & Slater, Intermediate Algebra, 5e - Slide #2 Square Roots The square root of a number is a value that.
Rational Exponents Fraction Exponents.
Sullivan Algebra and Trigonometry: Section R
Copyright © Cengage Learning. All rights reserved. Roots, Radical Expressions, and Radical Equations 8.
Note that the denominator of the exponent becomes the index and the base becomes the radicand. Example Write an equivalent expression using radical.
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