RADICALS

Properties of Surds

1

: nnDefinition a a

mnnm

aa1

mn a

n ma nnm maa

1

21616 441

821616 3344

3

840961616 44 343

n mmn aa

Jeff Bivin -- LZHS

Simplify the surds

. .n n na b a b

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For positif real numbers a and b

32 16.2 16. 2 4 2

3 294 3 49.6 3 49. 6 3.7. 6 21 6 3 32 3 8.4 33 8. 4 32 4

Simplify!!!!!

xxxx

Jeff Bivin -- LZHS

288 12 2

500 10 5

3 500 35 4

Algebraic Operation on Surds

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Addition and SubtractionSuppose, anda b R c R

a c b c = a b c

Ex 5 5 10 5 = 5 10 5 15 5

5 3 48 2 27 = 5 3 4 3 6 3 5 4 6 3 3 3

20 125 3 5 = 2 5 5 5 3 5 = 0

Algebraic Operation on Surds

Jeff Bivin -- LZHS

MultiplicationSuppose, and ,a b R c d R

. .a c b d ab cd=

Ex 5 5.10 2 = 5.10 5.2 50 10

3 2 3 2 3

2 5 5 3 2 = 2.5 2.3 5.2 =

6 6 2 5 2 6

10 6 10

Algebraic Operation on Surds

Jeff Bivin -- LZHS

DivisionSuppose, and ,a b R c d R

: : :a c b d a b c d=

Ex 5 8 :10 2 = 5 :10 8 : 214

2

5 2 5 2

3

2 2

5 2

3

1.2 12

2 3.3 2

12 6=

1

26 6

12 6=

31

3

Simplify!!!!!

Jeff Bivin -- LZHS

0,36 0,16 1

6 2 5 2 2 5 2 11 10

a b

a b

a b

Simplifying Surds expression and ( ) 2a b ab

( ) 2a b ab

2a b 2a b ab

2a b 2a b ab

a b 2a b ab

a b 2a b ab

Simplifying Surds expression and ( ) 2a b ab

( ) 2a b ab

2a b 2a b ab

2a b 2a b ab

a b 2a b ab

a b 2a b ab

Example!

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5 2 6 3 2 2 3.2 3 2

8 2 15 3 5 2 3.5 5 3

Try this Questions!!!

Jeff Bivin -- LZHS

3 2 2 1 2

7 2 10 5 2

8 48 6 2

14 6 5 9 5

0,3 0,08

1 1....

a b

a b

15

Rationalizing Fractions Involving Surds

Jeff Bivin -- LZHS

Consider!!

a b a b 2 2

a b a b

a a a

a b a b 22 2a b a b

2 2a b a b a b

Conjugate

Simplify

32

6

2

6

Jeff Bivin -- LZHS

3

30

9

30

3

3

3

10

3

10

Simplify

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5

5

5

32

5

12

5

12

10

24

10

24

Simplify

5

152

25

152

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7

23

223239

23

23

23

23

1

Simplify

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11

5312

11

543

5545416

543

54

54

54

3

Simplify

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3

71

6

712

7771

712

71

71

71

2

Simplify

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3321

332

332324

332

32

32

32

3

Simplify

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2

4

2

2

2

2

2

2

2

1

2

1 33 2

3 3

3 2

3 2

3 2

33

Simplify

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3

162

3

32

3

3

3

2

3

2 5

5 5

5 4

5 4

5 4

5

5

5

Simplify

Jeff Bivin -- LZHS

Try this Questions!!!

Jeff Bivin -- LZHS

5 630

5 6

......?

a b

a b

9

1

2 2 1

24

1 3...

4 12

Exponential Equations

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Properties

2 15 5

5x

12 1 25 5 5x

12 25 5x

3 27x 33 3x 3x 1 1

22 4

x x

3 6 3 13

27x 1x

B Ca a B C

Try this Questions!!!

Jeff Bivin -- LZHS

2 3 54 16x x 4x

2 23 7

13

27x

x

5

2x

13

2

3 1

0,091

0,3

x

x

2x

25 125x 1

2x

To be continued…

LOGARITMA