Roots and Radical Expressions

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Presentation transcript:

Roots and Radical Expressions 6-1

Objective To find the root.

Key Concept If , a and b are both real numbers and n is a positive integer, then a is the nth root of b. Radical Sign Index Radicand

Roots of Powers For any real number a, If n is odd If n is even

Principle Root There are two real roots of b. There is positive b, and negative b.

Finding all real roots What is the real cube root of 0.008? What is the real fourth root of -0.0001? Since -0.0001 is negative, there is no real fourth root.

What is the real cube root of ? What is the real fourth root of ?

Finding Roots: What is the real-number root? So, So,

Finding Roots: What is the real-number root? There is no real root because there is no real number whose fourth power is -1.

Simplifying Radical Expressions 4 4 2 2 2 2

Simplify Radical Expressions: Questions Answers

STEM The voltage V of an audio systems speakers can be represented by , where P is the power of the speaker. An engineer wants to design a speaker with 400 watts of power. What will the voltage be?

Definition of i The imaginary number, i, was invented so we can solve equations like: Remember, it’s Not a Real Number! It’s an Imaginary Number!

You can find any power of i Properties of i They repeat the first 4! You can find any power of i

Simplify Memorize the first 4 powers of i: Divide the exponent by 4 Your answer is i with the remainder as it’s exponent. Memorize the first 4 powers of i:

T.O.O. Simplify 1) 2) 4) 3)

Simplify 1) 2) Not a real number, but now have new definition Put the i in front of radical! i after integer Don’t write:

Homework Pg 364 # 11-29 Odd, 30, 45-48 ALL