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Understanding nth Roots and Rational Exponents in Algebra 3

This lesson covers the fundamental concepts of powers, roots, and radical expressions, focusing specifically on nth roots and rational exponents. Students will learn how to convert powers into radical form, evaluate roots by hand and with a calculator, and handle negative exponents. Through guided practice and hands-on exercises, learners will grasp how to rewrite expressions and solve problems involving exponents. Homework and worksheets are provided for additional practice, reinforcing today’s lessons in Algebra 3.

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Understanding nth Roots and Rational Exponents in Algebra 3

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Presentation Transcript

  1. Warm Up • Write down the best thing you did over the holiday break

  2. Algebra 3Chapter 7: POWERS, ROOTS, and RADICALSLesson 1: nth roots and rational exponents

  3. VOCAB • Index – is the number of the radical • nth root of a – is • All powers can be transformed into radical expressions • Examples we know so you solve it by doing the opposite which is a square root • If the power is bigger than 2 you do an nth root which means

  4. Rules • N is odd then a has one root • N is even and a > 0 then a has 2 real roots • N is even and a = 0 then a has 1 real root and it is 0 • N is even and a < 0 then a has 0 real roots but 2 imaginary roots

  5. TODAY • Today we will be learning how to write powers as exponential equations. In order to solve them you have to understand what they mean.

  6. Directions (Writing Roots) • Plug the numbers into the formula

  7. I DO (Writing Roots) • 1. n = 3 a = 8 • 2. n = 5 a = 7 • 3. n = 2 a = 6 • 4. n = 9 a = 12

  8. WE DO (Writing Roots) • 1. n = 6 a = 98 • 2. n = 7 a = 37 • 3. n = 3 a = 7 • 4. n = 13 a = 4

  9. YOU DO (Writing Roots) • 1. n = 5 a = 86 • 2. n = 71 a = 73 • 3. n = 21 a = 64 • 4. n = 13 a = 1296

  10. Directions (Rewriting Problems) • Use the formula to rewrite

  11. I DO (Rewriting Problems) • 1. • 2. • 3. • 4.

  12. WE DO (Rewriting Problems) • 1. • 2. • 3. • 4.

  13. YOU DO (Rewriting Problems) • 1. • 2. • 3. • 4.

  14. Review • Today you learned how to rewrite radical expressions

  15. Homework • Worksheet • 7.1A (1 – 24)

  16. Warm Up Rewrite • 1. • 2.

  17. Algebra 3Chapter 7: POWERS, ROOTS, and RADICALSLesson 1: nth roots and rational exponents

  18. TODAY • We will evaluate rationals by hand and in the calculator.

  19. Directions (HAND) • Think small to big. ROOT1 2 3 4 5 6 • 1 1 1 1 1 1 • 2 4 8 16 32 64 • 3 9 27 81 243 729 • 4 16 64 256 1024 4096 • 5 25 125 625 3125 15625 • 6 36 216 1296 7776 46656 • 7 49 343 2401 16807 117649

  20. Special Directions • When you have a negative exponent • Change the exponent to a positive • Flip the numerator and denominator • AKA reciprocal • EVEN POWERS NEED ± • EXCEPT when there is a negative out front

  21. I DO (Hand) • Evaluate the expression by hand 1. 2. 3. 4.

  22. WE DO (Hand) • Evaluate the expression by hand 1. 2. 3. 4.

  23. YOU DO (Hand) • Evaluate the expression by hand 1. 2. 3. 4.

  24. Directions (Calculator) • Write the problem in exponent form • Type in the calculator • Remember the ^ is for big powers • Remember you need parenthesis for negatives and fractions • ROUND to 2 decimals

  25. I DO (Calculator) • Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.

  26. WE DO (Calculator) • Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.

  27. YOU DO (Calculator) • Evaluate using the calculator and then round to 2 decimals. • 1. • 2. • 3. • 4.

  28. Review • What did you learn today?

  29. Homework • Worksheet • 7.1 (25 – 45)

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