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Evaluate nth Root and Use Rational Exponents. Notes 1 – Section 6.1. Essential Learnings. Students will understand and be able to apply the rules of exponents and number properties of algebraic expressions to solve problems. Real nth Roots of a.

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essential learnings
Essential Learnings
  • Students will understand and be able to apply the rules of exponents and number properties of algebraic expressions to solve problems.
real nth roots of a
Real nth Roots of a
  • Let n be an integer (n>1) and let a be a real number.

If n is an even integer:

a<0 No real nth roots

a=0 One real nth root

a>0 Two real nth roots

real nth roots of a1
Real nth Roots of a
  • Let n be an integer (n>1) and let a be a real number.

If n is an odd integer:

a<0 One real nth roots

a=0 One real nth root

a>0 One real nth roots

rational exponents
Rational Exponents

Let be an nth root of aand let mbe a positive integer.

rational exponents1
Rational Exponents

Let be an nth root of aand let m be a negative integer.

example 1 7 9 in assign
Example 1 (7 & 9 in Assign.)

Rewrite the expression using rational exponent notation.

example 2 11 13
Example 2 (11 & 13)

Rewrite the expression using radical notation.

example 3 15 17 19
Example 3 (15, 17, 19)

Find the indicated real nth root of a.

n = 6, a= 4096 n = 3, a= -27

example 4 21 33
Example 4 (21-33)

Evaluate the expression without using a calculator.

example 5 36 42
Example 5 (36-42)

Approximating Roots - Evaluate the expression using a calculator. Round to two decimal places.

example 6 49 57
Example 6 (49-57)

Solve the equation. Round to two decimal places.

example 7 49 57
Example 7 (49-57)

Solve the equation. Round to two decimal places.

assignment
Assignment

p. 417: 3-31odd, 36-42 (x3), 49-57 (x3)

Signed Syllabus / Honor Code Slip

Covered Textbook