1. 1. 2. 3. 4. 5. Find the degree of the expressions: a)b)

3.  A radical expression contains a square root.  A radicand, the expression under the radical sign, is in simplest form if it contains no perfect square factors other than 1.  Using prime factorization we can simplify radical expressions. Radical or Square Root  Radicand

4.  X 2 = ______  16 = _______  49 = _______

7.  Examples: 1. 2.

9. 3. 4.

10.  “Rational” means ratio of two integers, or fraction.  So a variable or number with a rational exponent will look like this….  So what does this have to do with radicals?

11. XY 11 42 93 164 255 XY 1 4 9 16 25

12. XY 1 8 27 64 XY 1 8 2

13.  So what would we do if we had a variable to the ¼ power?

14.  Why ¼ ? FORMULA:

15.  So radicals can be re-written as exponents! Re- write each one with a rational exponent… 1) 2) 3)

16.  Re-write each rational exponent as a radical… 4) 5) 6)

17. XY 1 8 27 64 XY 1 8 27 64

18.  Why 2/3?

19.  Re-write each radical as a rational exponent… 1) 2) 3)

20.  Re-write each rational exponent as a radical… 4) 5) 6)

21. Example 1: Example 2:

22. Example 1: Example 2:

23. 1: 2:

24. Example 1 (perfect square): Example 2 (with leftovers): Since this is a 3 rd root you find three in your “pairs” not just two!

25. 1) 2)

28. 1) 2)

29. Worksheet Bring in your Parent Forms!

30. Simplify. Write with a rational exponent Write in radical form, then simplify.

33.  In order to add/subtract radicals, the _____________ must be the same.  To add/subtract radicals, simply add/subtract the________________.

37.  Find the perimeter of the rectangle below in radical form:

38.  Find the perimeter of the square below in radical form:

40.  To multiply monomial radicals (radicals that only have one term), multiply their “outsides” together then multiply their “insides” together. Make sure you SIMPLIFY the radical!

41.  Don’t forget to simplify the product, when possible!

42.  Don’t forget to simplify the product, when possible.

43.  Find the area of the following triangle:

44.  How can we simplify these?

47.  We can never leave a radical in the denominator of a fraction.  In order to get rid of a radical in the denominator, we have to “rationalize” the denominator.  In other words, we need to get the “rat” (radical) out of the “den” (denominator).

48.  What operation cancels radicals?  What is ?

49.  Are we allowed to just randomly multiply the denominator by something?  What are we allowed to multiply by without changing the problem?

51.  Don’t forget to simplify your final answers!

52.  Don’t forget to simplify your final answers.

54. Worksheet