simplify and add radicals

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