1. Bell Ringer
Name all of the sets of numbers to which each real number belongs. Natural, Whole, Integer, Rational, Irrational #1. 4 #2. 3/5 #3. -7/2 #4. √26

2. Supply Check I have decided to announce the first supply check.
This will happen on FRIDAY, OCTOBER 24
I will be looking for pencil, piece of paper, calculator, and red pen.

3. Continue 10. 1 and 10.2 Radicals and Real Numbers
R drive > Key > Week 11 > Wednesday > Finish 10.1 and 10.2
File > Save As > P drive > math > Week Finish 10.1 and 10.2

4. Simplifying Radicals

5. Vocabulary
Radical Expression – An expression that contains a square root
Radicand – the expression under the radical sign

6. Notes Product Property of Square Roots:
A radicand is in simplest form if it contains no perfect square factors other than 1. The following property can be used to simplify square roots.
Product Property of Square Roots:
For any numbers a and b, where a ≥ 0 and b ≥ 0, the square root of the product ab is equal to the product of each square root.
Symbols:
Example:
The Product Property of Square Roots and prime factorization can be used to simplify radical expressions in which the radicand is not a perfect square.

7. Simplify Square Roots: Example 1)
= step one: prime factorization of 12
step twp: product property of sq roots
step three: simplify

8. Your turn: Remember the steps……
step one: prime factorization
step two: product property of sq roots
step three: simplify
Example 2)

9. The product property can also be used to multiply square roots: Multiply Square Roots Example 3) Find

10. Your turn: remember the steps 2b)

11. A fraction containing radicals is in simplest form if 1) no prime factors appear under the radical sign with an exponent greater than 1 and if ) no radicals are left in the denominator. Rationalizing the denominator of a radical expression is a method used to eliminate radicals from the denominator of a fraction.

12. Rationalizing the Denominator:
3a) Simplify step one: multiply by a fraction with the
denominator of this fraction in
its numerator and denominator.
• = (I will explain)
step two: simplify if necessary

13. Your turn: remember the steps 3b)

14. More Practice:
Simplify: Write problems and show work on notebook paper.
1) ) )
4) )
6) )

15. Example 3 Compare Real Numbers

16. Example 4 Compare Real Numbers

17. Your Turn Practice Comparing Real Numbers

18. Example 5 Order Real Numbers

19. Example 6 Order Real Numbers

20. Your Turn Practice Ordering Real Numbers

21. Example 7 Solve Equations

22. Example 8 Solve Equations
Solve each equation. Round to the nearest tenth, if necessary.
W2 = 169
R2 = 50

23. Your Turn Practice Solving Equations

24. Example 9 Use Real Numbers to Solve Problems

25. Example 10 Use Real Numbers to Solve Problems
The formula for aspect ratio R is R = s2/A, where s is the wingspan in feet and A is the area of the wing. What is the wingspan of a hang glider if the aspect ratio is 6.4 and the area of the wing is 40 square feet?

26. Your Turn Practice Using Real Numbers to Solve Problems

27. Homework Section 10.1 #1-13

28. Homework Section 10.1 #1-13