1. War m up
Simplify

2. War m up solutions

3. SIMPLIFY
RADICALS

4. Review of the basics
In the expression 64,
is the radical sign and
64 is the radicand.
1. Find the square root: 64
8
2. Find the square root: − 100
-10

5. 3. Find the squar e ± 121
r oot:
11, -11
4. Find the square root: 441
21
25
5. Find the square root: − 81
5
−
9

6. W hat number s ar e
perfect squar es?
1•1=1
2•2=4
3•3=9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, ...

7. 1. Simplify 147
Find a perfect square that goes into
147.
147 = 49g3
147 = 49 g 3
147 = 7 3

8. 2. Simplify
605
Find a perfect square that goes into
605.
121g5
121g 5
11 5

9. Simplify
72
A. 2 18
B. 3 8
C. 6 2
D. 36 2
.

10. Perfect Square Factor * Other Factor
18 = 9× 2 = 3 2
LEAVE IN RADICAL FORM
288 = 144 × 2 = 12 2
75 = 25 3 = 5 3
24 = 4× 6 = 2 6
72 = 36 × 2 = 6 2

11. 4. Simplify 49x 2
Find a perfect square that goes into
49.
49 g x 2
7x
5. Simplify 8x = 8 g x
25 25
2 2 g x 24 x
24
2 2gx 2
x
2 x12 2 x

12. Simplify 36
9x
A.3x6
B.3x18
C.9x6
D. 9x18
Worksheet #5 try #1, 8, 12

13. Intermediate Simplification Cube roots!!!!
Simplify: Simplify:
Simplify: Is this possible?? 3 6
54n 9 563
3
−8 ? Find a perfect cube that goes
Into 54…..
How about 9 ×3 8 ×3 7
−2 ×−2 ×−2
3
27 ×3 2 ×3 n6
3
6 18 7
3
−8 = − 2 3 ×3 2 ×n 3
Don’t forget
Worksheet #5 23 to use the
Try #3, 10, 14
3n 2 proper
index!

14. Answer s:
3. − 3 6 3
3
10. 2m 3
14. − 2ab 23
2b 2

15. Intermediate Simplification - 4 th roots
Simplify: Simplify:
Simplify: Is this possible??
4 20
32n
4
−256 ? Find a perfect forth root
−2 324v
4 6
that goes into 32…..
How about
−2 ×4 81 ×4 4 ×4 v 4 ×4 v 2
−4 ×−4 ×−4 ×−4
4
16 ×4 2 ×4 n 20
4
= 256 2 × 2 ×n
4
20
4 − 2 ×3 × 4 ×v4 44
v 2
Make a
conclusion 54 −6 v 4 v 4 2
about 2n 2
negative
WS #5 Don’t forget to use
radicands.
the proper index!
Try 7, 13, 15

16. Answer s:
24
7. 2n 8
3 2
13. 3 5 x y
4
3 3
15. 2 xy 8 x y4

17. Intermediate Simplification - 5 th roots
Simplify: Simplify:
Simplify: Is this possible?? 5 20
6250n 5 13
5
−32 ? Find a perfect fifth root
3 1215v
that goes into 6250…..
How about
3 ×5 243 ×5 5 ×5 v10 ×5 v 3
−2 ×−2 ×−2 ×−2 ×−2 5
3125 ×5 2 ×5 n 20
10
5
−32 = −2 20
3 ×3 × 5 ×v
5 5 5
v 3
Make a
5 × 2 ×n
4 5
conclusion 25 3
about 45 9v 5v
negative 5n 2
radicands
WS #5 Don’t forget to use
and indexes.
the proper index!
Try 9, 17

18. Answer s:
5 2
9. 2r 7 r
17. 2 xy 7 xy 6
½ sheet simplify – Pick 10 – make sure you pick different
indexes – self check at the back table – Homework check

19. Simplifying Radicals
• ½ sheet simplify – Pick 10 – make sure
you pick different indexes –
• self check at the back table –
• Homework check
• Review #5

20. +
To add or subtact radicals: combine
the coefficients of like radicals(same
index and same radicand)

21. Simplify each expression
Use what you know: add or subtract coefficients of like terms
6 x + 5 x − 3x = 8 x
6 7 +5 7 −3 7 = 8 7
5 6 +3 7 + 4 7 −2 6 = 3 6+7 7

22. Simplify each radical first and then combine
like radicals.
2 25 ×2 − 3 16 ×2 =
2 50 − 3 32 =
2 ×5 2 − 3 ×4 2 =
10 2 − 12 2 =
−2 2

23. Simplify each radical first and then combine like radicals.
3 27 + 5 48 =
3 9 × + 5 16 × =
3 3 Simplify each radical
3 × 3 + 5 ×4 3 =
3 multiply
9 3 + 20 3 = Add like radicals (like terms)
29 3

24. Simplify each expression
6 5 +5 6 −3 6 =
3 24 + 7 54 =
2 8 − 7 32 =
Adding Subtracting worksheet # 3 – multiples of 3

25. Intermediate Add/Subtract radical
expressions
GROUP 1 GROUP 2
4 80 + 2 20 − 3 45
5 6 − 3 24 + 150
=5 6 − 3 4 6 + 25 6 4 16 5 + 2 4 5 − 4 9 5
= 5 6 − 3 ×2 × 6 + 5 6 4 ×4 × 5 + 2 ×2 × 5 − 4 × × 5
3
=5 6 − 6 6 + 5 6 16 5 + 4 5 − 12 5
4 6 11 5

26. Intermediate Add/Subtract radical
expressions
GROUP 1 GROUP 2
4 80 + 2 20 − 3 45
5 6 − 3 24 + 150
=5 6 − 3 4 6 + 25 6 4 16 5 + 2 4 5 − 4 9 5
= 5 6 − 3 ×2 × 6 + 5 6 4 ×4 × 5 + 2 ×2 × 5 − 4 × × 5
3
=5 6 − 6 6 + 5 6 16 5 + 4 5 − 12 5
4 6 11 5