Radical Expressions MATH 018 Combined Algebra S. Rook

2 Overview Section 10.1 in the textbook: –Finding square roots –Finding cube roots –Finding n th roots

3 Finding Square Roots

44 Should be a review for numbers: means “what number multiplied by itself gives you a”? What is the value of ? What about the square root of a negative number? –Suppose we want to evaluate The square root of a negative number does NOT exist in the real number system because the product of two negatives is positive!

55 Finding Square Roots (Continued) Not any more difficult for variables: –Consider evaluating –What times itself will yield x 4 ? –Can also see by expanding x 4 Thus if a is divisible by 2 You will find it beneficial to memorize AT LEAST the first ten perfect squares

Finding Square Roots (Example) Ex 1: Evaluate in the REAL number system if possible: a)d) b) c) 6

7 Finding Cube Roots

88 Should be a review for numbers means “what number multiplied by itself three times gives you a”? What is the value of ? What about the cube root of a negative number? –Suppose we wish to evaluate The cube root of a negative number EXISTS in the real number system because the product of three negatives is negative

99 Finding Cube Roots (Continued) Not any more difficult for variables: –Consider evaluating –What times itself will three times yields x 9 ? –Can also see by expanding x 9 Thus if a is divisible by 3 You will find it beneficial to memorize AT LEAST the first five perfect cubes

Finding Cube Roots (Example) Ex 2: Evaluate in the REAL number system if possible: a)d) b) c) 10

11 Finding n th Roots

12 Finding n th Roots Should be a review for numbers means “what number multiplied by itself n times gives you a”? How would we evaluate ? What about the n th root of a negative number? –How would we evaluate ?

13 Finding n th Roots (Continued) –Can extend this to the general case: The product of an even number of negatives is positive –Therefore, the even root of a negative number does NOT exist in the real number system The product of an odd number of negatives is negative –Therefore, the odd root of a negative number DOES exist in the real number system

Finding n th Roots (Example) Ex 3: Evaluate in the REAL number system if possible: a)d) b) c) 14

15 Summary After studying these slides, you should know how to do the following: –Find square roots –Find cube roots –Find n th roots Additional Practice –See the list of suggested problems for 10.1 Next lesson –Rational Exponents (Section 10.2)