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Similar to 3-2_radical_expressions_and_rational_exponents.ppt
3-2_radical_expressions_and_rational_exponents.ppt
- 1. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Rewrite radical expressions by using rational exponents. Simplify and evaluate radical expressions and expressions containing rational exponents. Objectives
- 2. Holt Algebra 2 3-2Radical Expressions and Rational Exponents index rational exponent Vocabulary
- 3. Holt Algebra 2 3-2Radical Expressions and Rational Exponents The nth root of a real number a can be written as the radical expression , where n is the index (plural: indices) of the radical and a is the radicand. When a number has more than one root, the radical sign indicates only the principal, or positive, root. n When a radical sign shows no index, it represents a square root. Even roots MUST be a positive Answer. Reading Math
- 4. Holt Algebra 2 3-2Radical Expressions and Rational Exponents A rational exponent is an exponent that can be expressed as , where m and n are integers and n ≠ 0. Radical expressions can be written by using rational exponents. m n
- 5. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Method 1 Evaluate the root first. (4)1 Write with a radical. 64 1 3 4 Evaluate the root. Evaluate the power. Check It Out! Example 3a Write the expression in radical form, and simplify. Method 2 Evaluate the power first. Write will a radical. 4 Evaluate the power. Evaluate the root. ( ) 1 3 64 ( )1 3 64 3 64
- 6. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Method 1 Evaluate the root first. (2)5 Write with a radical. 4 5 2 32 Evaluate the root. Evaluate the power. Check It Out! Example 3b Write the expression in radical form, and simplify. Method 2 Evaluate the power first. Write with a radical. 32 Evaluate the power. Evaluate the root. ( ) 5 2 4 ( )5 2 4 2 1024
- 7. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Write each expression by using rational exponents. Simplify. a. b. 3 4 81 10 3 Check It Out! Example 4 9 3 10 1000 Simplify. 5 1 2 c. 2 4 5
- 8. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Method 1 Evaluate the root first. (5)3 Write with a radical. 625 3 4 125 Evaluate the root. Evaluate the power. Check It Out! Example 3c Write the expression in radical form, and simplify. Method 2 Evaluate the power first. Write with a radical. 125 Evaluate the power. Evaluate the root. ( ) 3 4 625 ( )3 4 625 4 244,140,625
- 9. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Simplify the expression. Assume that all variables are positive. Check It Out! Example 2a Product Property. Simplify. Factor into perfect fourths. 2 x 2x 4 4 16x 4 24 • 4 x4 4 24 •x4
- 10. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Find all real roots. a. fourth roots of –256 A negative number has no real fourth roots. Check It Out! Example 1 b. sixth roots of 1 A positive number has two real sixth roots. Because 16 = 1 and (–1)6 = 1, the roots are 1 and –1. c. cube roots of 125 A positive number has one real cube root. Because (5)3 = 125, the root is 5.
- 11. Holt Algebra 2 3-2Radical Expressions and Rational Exponents When an expression contains a radical in the denominator, you must rationalize the denominator. To do so, rewrite the expression so that the denominator contains no radicals. Remember!
- 12. Holt Algebra 2 3-2Radical Expressions and Rational Exponents The properties of square roots in Lesson 1-3 also apply to nth roots.
- 13. Holt Algebra 2 3-2Radical Expressions and Rational Exponents
- 14. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Check It Out! Example 2b Quotient Property. Product Property. Rationalize the numerator. Simplify. Simplify the expression. Assume that all variables are positive. 8 4 4 3 x 4 2 27 3 x
- 15. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Check It Out! Example 2c 3 3 7 2 x x Product Property of Roots. Simplify. Simplify the expression. Assume that all variables are positive. x3 3 9 x
- 16. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Rational exponents have the same properties as integer exponents (See Lesson 1-5)
- 17. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Product of Powers. Simplify each expression. Simplify. Evaluate the Power. 6 Check It Out! Example 5a Check Enter the expression in a graphing calculator.
- 18. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Simplify each expression. (–8) – 1 3 Check It Out! Example 5b 1 –8 1 3 1 2 – Negative Exponent Property. Evaluate the Power. Check Enter the expression in a graphing calculator.
- 19. Holt Algebra 2 3-2Radical Expressions and Rational Exponents Quotient of Powers. Simplify each expression. Simplify. Evaluate the power. 5 2 Check It Out! Example 5c 25 Check Enter the expression in a graphing calculator.