1. 5.4 Irrational Numbers

2. Irrational numbers Irrational numbers are those that cannot be written as a fraction Irrational numbers have non-terminating or non-repeating decimals The square root of any prime number is irrational π is irrational

3. Not every square root is irrational Numbers like 36 and 81 are called perfect squares

4. Perfect squares 0 2 = 0 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 11 2 = 121 12 2 = 144 13 2 = 169 14 2 = 196 15 2 = 225

5. Simplifying square roots Product rule

6. Examples: Simplify

7. Multiply

8. Dividing square roots

9. Examples: Divide

10. Addition/Subtraction To add or subtract square roots the radicand (the number under the radical) must be the same Then add/subtract the numbers in front of the radicals

11. Examples: Add or subtract

12. More addition If the radicands are different try to simplify first

13. Examples: Simplify then add

14. Rationalizing If there is a radical in the denominator of a fraction you can simplify or rationalize by multiplying both the numerator and the denominator by the radical

15. Examples: Rationalize

16. Other roots

17. HW: p. 234/1-66 evens