1. Unit 2 Section 1 Simplifying Radicals Day 1

2. Perfect Squares 12 = 22= 32= 42= 52= 62= 72= 82= 92= 102 112 = 122=
121
12 =
22=
32=
42=
52=
62=
72=
82=
92=
102
112 =
122=
132=
142=
152=
162=
172=
182=
192=
202= 4
144 9
169 16
196 25
225 36
256 49
289 64
324 81
361
100
400

3. How to Simplify Radicals
If the number is a perfect square, just take the square root of the number
If not :
Using multiplication, break down the radicand into 2 numbers
1st number being the HIGHEST perfect square that divides into the radicand

4. Examples
1.) 16
2.) 144
3.) 324

5. 4.) 8
5.) 63

6. 6.) 12
7.) 200
8.) 128

7. 9.) 80
10.) 42
11.) 50

8. 12.) 288
13.) 512
14.) 30

9. Simplifying Radicals Day 2

10. REVIEW Simplify
A. .
B. .
C. .
D. .

11. REVIEW Simplify
A. .
B. .
C. .
D. .
100 5

16. Simplifying Radicals as Fractions
Divide the numerator by the denominator and simplify OR
Take the square roots of the numerator and denominator separately

17. There is a radical in the denominator!
1. Simplify.
Divide the radicals.
Uh oh…
There is a radical in the denominator!
Whew! It simplified!

18. 2. Simplify

19. 3. Simplify

20. 4. Simplify

21. 5. Simplify

22. 6. Simplify

23. Simplifying Square Roots Day 3

24. What makes 39𝑥 equivalent to 3 39 ?

25. What makes 6 15𝑥 equivalent to 36 15 ?

26. What makes 2 17𝑥 equivalent to 8 17 ?

27. For what value of x should the expression be simplified?
35𝑥
x = 22
x = 13
x = 15
x = 26

28. For what value of x should the expression be simplified?
77𝑥
x = 15
x = 21
x = 39
x = 51

29. For what value of x should the expression be simplified?
235𝑥
x = 13
x = 34
x = 118
x = 65

30. For what value of x is 28𝑥 2 equal to 7 2 ?14 28

31. For which value of x is the expression 180 𝑥 equal to a whole number?4 5 18 25