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Working With Radicals

Working With Radicals. Do Now. Simplify each of the exponential expressions. You know these rules. Let’s look at how we can work with expressions such as . Open the TI-NSPIRE File. Let’s look at some table values for x 1/2 .

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Working With Radicals

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  1. Working With Radicals

  2. Do Now Simplify each of the exponential expressions

  3. You know these rules

  4. Let’s look at how we can work with expressions such as

  5. Open the TI-NSPIRE File • Let’s look at some table values for x1/2. • Look for some special values you might recognize. What would be another way to express x1/2? • Look at a graph and click on the line to see what graph has been plotted.

  6. Some things your observed How can you rewrite each of the following with a fractional exponent?

  7. So we know that

  8. Open the TI-NSPIRE File • Let’s look at some table values for x1/3. • Look for some special values you might recognize. What would be another way to express x1/3? • Look at a graph and click on the line to see what graph has been plotted.

  9. Some things your observed How can you rewrite each of the following with a fractional exponent?

  10. So we know that

  11. Open the TI-NSPIREFile • Let’s look at some table values for x1/4. • Look for some special values you might recognize. What would be another way to express x1/3? • Look at a graph and click on the line to see what graph has been plotted.

  12. Some things your observed How can you rewrite each of the following with a fractional exponent?

  13. So we know that

  14. Which problems can you rewrite? Now let’s find out how we look at the others!

  15. Open the TI-NSPIREFile • Let’s look at some table values for 4x, such as 41, 41.5, 42, 42.5, 43, 43.5, 44, etc. • Look for some special values you might recognize like 41, 42, 43, 44. • Look at the value for x = 1.5. Remember this is 41.5. What fractional power could replace 1.5?

  16. To find a value for we need to do a little math.

  17. Look at x = 2.5

  18. Try changing

  19. Open the TI-NSPIREFile • Let’s look at some table values for 16x, such as 161, 161.5, 162, 162.5, 163, 163.5, 164, etc. • Look for some special values you might recognize. First look at 161, 162, 163 • Look at the value for x = 1.25. What fraction could replace 1.25?

  20. Simplify

  21. So how could we rewrite

  22. Simplify each expression:

  23. Simplify each expression:

  24. Simplify each expression:

  25. Now can you simplify the rest?

  26. Simplify these

  27. Using the new ideas to solve equations These statements state that the cube root of some number is 4. What operation will undo the cube root? We’ll cube both sides. üOur solution checks

  28. Solve this equation These statements are the same. How can we undo raising a number to the 4/3 power? We’ll raise each side to the ¾ power üOur solution checks

  29. Solve this equation These statements are the same. How can we undo raising a number to the 4/3 power? We’ll raise each side to the power of 4 üOur solution checks

  30. Solve this equation These statements are the same. How can we undo raising a number to the 4/3 power? We’ll raise each side to the power of 3 üOur solution checks

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