3. Introduction to Irrational Numbers

5. We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.” √ 3 is an irrational number. √ is the radical sign / symbol, and 3 is called the radicand.

6. HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

7. In the expression, is the radical sign and 64 is the radicand. If x 2 = y then x is a square root of y. 1. Find the square root: 8 2. Find the square root: -0.2

8. 3. Find the square root: 11, -11 4. Find the square root: 21 5.Find the square root:

9. 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6.82, -6.82

10. What numbers are perfect squares? 1 1 = 1 2 2 = 4 3 3 = 9 4 4 = 16 5 5 = 25 6 6 = 36 49, 64, 81, 100, 121, 144,...

11. The square root of 4 is 2

12. The square root of 9 is 3

13. The square root of 16 is 4

14. The square root of 25 is 5

15. 1. Simplify Find a perfect square that goes into 147.

16. 2. Simplify Find a perfect square that goes into 605.

17. Simplify A.. B.. C.. D..

18. Now you try some…

19. Now you try…

20. How do you simplify variables in the radical? Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

21. 4. Simplify Find a perfect square that goes into 49. 5. Simplify

22. Simplify 1.3x 6 2.3x 18 3.9x 6 4.9x 18

23. Now you try some…

24. Adding & Subtracting Radicals The rules for adding and subtracting radicals are very similar to the rules for adding and subtracting polynomials. The radical / radicand have to match exactly in order to add or subtract.

25. Ex. 1:

26. Ex. 2:

27. Now you try some…

28. IMPORTANT If each radical in a radical expression is not in simplest form, simplify them first. Then use the distributive property, whenever possible, to further simplify the expression.

29. Ex. 4:

30. Ex. 5: Simplify, then use a calculator to verify your answer.

31. Ex. 6: Simplify, then use a calculator to verify your answer.

32. Now you try some…

33. Rational or Irrational? Justify your answer.