1. Warm-up Estimate the following to the thousandths place. 187.6539
3.8537
0.0007

2. Intro to Radicals

3. What is a radical?

4. Radicals A radical can be a square root, cubed root, fourth root, etc!
Inverse operation of exponents
Just like we “undo” addition with subtraction, and “undo” multiplication with division, we “undo” exponents with radicals!

5. What are perfect squares

6. Estimating Square Roots
What happens when the radicand is not a perfect square, cube, etc?

7. Estimating Square Roots
The square root has to be in between two integers. So think about the perfect squares that are above or below the number.
Example: 55
So 55 is between 49 and 64, so therefore the has to be between 7 and 8.

8. Estimating Square Roots
Example: 90
Example: 80
Example: 105

9. Estimating Square Roots: Application
You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest inch.
500 = approximately 22 inches so you will need about 88 inches of fringe

10. Estimating Square Roots: Application
You want to build a fence around a square garden that is 250 square feet. Calculate the length of one side of the garden and the total length of the fence.
250 = approximately 16 ft

11. Estimating Square Roots: Using Calculator
Example: 141
Example: 154
Example: 600
Example: 800

12. What do we do if radicals are NOT perfect squares?
SIMPLIFY THEM!

13. Radicals are in SIMPLEST FORM
1. No perfect square factors other than 1 are under the radical.
2. No fractions are under the radical.
3. No radicals are in the denominator.

14. To simplify radicals (with numbers under the radical):
Create a Factor Tree- circle ALL prime numbers
Write all prime factors under the radical
Circle any pairs
Move ONE of each pair to the front
Multiply remaining numbers if necessary

15. Step 1: Create factor trees to find prime factors
What are prime numbers?
A number greater than one that only has the factors of one and itself!
2, 3, 5, 7, 11, 13, …

16. Factor Trees to Prime Factorization45

17. Factor Trees to Prime Factorization54

18. Factor Trees to Prime Factorization98

19. When you have a pair, bring the number out.
EX:1 Simplify.
When you have a pair, bring the number out.

20. When you have a pair, bring the number out.
EX:2 Simplify
When you have a pair, bring the number out.

21. EX:3

22. EX:4 Simplify.

23. You try!