simplify and add radicals
TRANSCRIPT
Warm up Warm up
Simplify
Warm up solutionsWarm up solutions
SIMPLIFY SIMPLIFY RADICALSRADICALS
In the expression , is the radical sign and
64 is the radicand.
1. Find the square root:1. Find the square root:
88
2. Find the square root:2. Find the square root:
-10-10
64
64
100
Review of the basicsReview of the basics
11, -1111, -11
4. Find the square root:4. Find the square root:
2121
5.5. Find the square root:Find the square root:
3. Find the square root: 3. Find the square root: 121
441
25
815
9
1 • 1 = 1 • 1 = 112 • 2 = 2 • 2 = 443 • 3 = 3 • 3 = 99
4 • 4 = 4 • 4 = 16165 • 5 = 5 • 5 = 25256 • 6 = 6 • 6 = 3636
49, 64, 81, 100, 121, 144, ...49, 64, 81, 100, 121, 144, ...
What numbers are perfect What numbers are perfect squares?squares?
1. Simplify 1. Simplify
Find a perfect square that goes into Find a perfect square that goes into 147.147.
147
147 349
147 349
147 7 3
2. Simplify2. Simplify
Find a perfect square that goes into Find a perfect square that goes into 605.605.
605
121 5
121 5
11 5
SimplifySimplify
A.A.
B.B.
C.C.D. D. ..
2 18
72
3 8
6 236 2
18
288
75
24
72
=
= =
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
9 2 3 2
144 2 12 2
25 3 5 3
4 6 2 6
36 2 6 2
Find a perfect square that goes into Find a perfect square that goes into 49.49.
4. Simplify4. Simplify 49x2
249 x7x
5. Simplify 258x 258 x 24
24
2
12
2 2
2 2
2 2
x x
x x
x x
SimplifySimplify 369x
A.3xA.3x66
B.3xB.3x1818
C.9xC.9x66
D. 9xD. 9x1818
Worksheet #5 try #1, 8, 12
Intermediate Intermediate Simplification Cube Simplification Cube roots!!!!roots!!!!
Simplify: Is this possible??Simplify: Is this possible??
3 8 ?3 654n
3 633 227 n How about
2 2 2 6
3 33 2 n
2 33 2n
39 56
Simplify: Simplify:
Find a perfect cube that goesInto 54….. 3 39 8 7
318 7
Worksheet #5
Try #3, 10, 14
Don’t forget to use the
proper index!
3 8 2
Answers:Answers:
3
3
2 23
3. 3 6
10. 2 3
14. 2 2
m
ab b
Intermediate Intermediate Simplification - 4Simplification - 4thth roots roots
Simplify: Is this possible??Simplify: Is this possible??
246 4v v
4 256 ?204 32n
20444 216 n How about
4 4 4 4 20
4 42 2 n
5 42 2n
642 324v
Simplify: Simplify:
Find a perfect forth root that goes into 32…..
4 24 4442 81 4 v v
4244 42 3 4 v v
Make a conclusion
about negative
radicands.Don’t forget to use the proper index!
WS #5
Try 7, 13, 15
256
Answers:Answers:
2 4
3 24
3 34
7. 2 8
13. 3 5
15. 2 8
n
x y
xy x y
Intermediate Intermediate Simplification - 5Simplification - 5thth roots roots
Simplify: Is this possible??Simplify: Is this possible??
2 359 5v v
5 32 ?205 6250n
20555 23125 n How about
2 2 2 2 2
204 55 2 n
4 55 2n
1353 1215v
Simplify: Simplify:
Find a perfect fifth root that goes into 6250…..
10 35 55 53 243 5 v v
10355 53 3 5 v v
Make a conclusion
about negative
radicands and indexes.
Don’t forget to use the proper index!
WS #5
Try 9, 17
5 32 2
Answers:Answers:
25
6
9. 2 7
17. 2 7
r r
xy xy
½ sheet simplify – Pick 10 – make sure you pick different indexes – self check at the back table – Homework check
Simplifying RadicalsSimplifying Radicals
• ½ sheet simplify – Pick 10 – make sure you pick different indexes –
• self check at the back table –
• Homework check
• Review #5
+To add or subtact radicals: combine the coefficients of like radicals(same index and same radicand)
Simplify each expressionSimplify each expression
737576 78
62747365 7763
6 5 3 8x x x x
Use what you know: Use what you know: add or subtract coefficients of like add or subtract coefficients of like termsterms
Simplify each radical first and then Simplify each radical first and then combine like radicals.combine like radicals.
3235022 25 2 3 16 2
2 5 2 3 4 2
10 2 12 2
2 2
Simplify each radical first and then combine like Simplify each radical first and then combine like radicals.radicals.
485273
3 9 3 5 16 3
3 3 3 5 4 3
9 3 20 3
29 3
Simplify each radical
multiply
Add like radicals (like terms)
Simplify each expressionSimplify each expression
636556
547243
32782
Adding Subtracting worksheet # 3 – multiples of 3
Intermediate Intermediate Add/Subtract radical Add/Subtract radical expressionsexpressions
5 6 3 24 150
=5 6 3 4 6 25 6
=5 6 6 6 5 6
5 6 3 2 6 5 6
4 6
4 80 2 20 3 45
GROUP 1 GROUP 2
4 16 5 2 4 5 4 9 5
4 4 5 2 2 5 4 3 5
16 5 4 5 12 5
11 5
Intermediate Intermediate Add/Subtract radical Add/Subtract radical expressionsexpressions
5 6 3 24 150
=5 6 3 4 6 25 6
=5 6 6 6 5 6
5 6 3 2 6 5 6
4 6
4 80 2 20 3 45
GROUP 1 GROUP 2
4 16 5 2 4 5 4 9 5
4 4 5 2 2 5 4 3 5
16 5 4 5 12 5
11 5