Guise 3 Radicals

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

Guide # 3 Room: ___________ TOPIC: RADICALS

Name: __________________________________ Date: _______________ ID #: _______________

3.1 Simplifying Radicals 3.2 Addition and Subtraction of Radicals 3.3 Multiplication of Radicals 3.4 Division and RationalizationSimplifying Radicals Write the name of each element of a radical in the following lines.

2

3

16

A radical expression is an exponential fraction expression. How can I prove that the following expression is true

xx

1 2

?

Square both sides of the expression. Remember the Law of Exponents that states

( x m ) n  x mn

( x )  (x )
2

1 2 2

xx xx xx

1 2 2 2 2x  x1

1

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

The equality remained the same and therefore we can conclude that the expression is true.

xx

1 2

.

Another way of proving that the previous expression is true is assigning a numeric value to x, for example 4. Use your calculator to provethat

4  2 and also that

4  2.
2

1 2

Let’s prove that

3

42  4 3 .

( 4 )  (4 )
3 2 3

2 3 3

4 4
2

2 3 3 6 3

4 4
2

42  42 16  16
Check your answer with your calculator. We can conclude that a radical expression can be written as an exponential fraction, where the exponent is the numerator and the index of the radical is the denominator. Write theexponential fraction as a radical expression.
4

Example:

5 3  3 54

1

1. 2 2

1

2. 4 3

3. 6

2

3

4. 8

1 3

2

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

5. 64

5

6

3

6. 9 5

7. 8

5 2

4

8. 10 3

9. 5

1 5

7

12 4
Write the radical expression as anexponential fraction expression. Example: 1.
4
3

6 6

1 3

52

2.

5

103

3.

2

45

4.

3

124

3

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

5.

163

6.

6

a4

7.

10

78

8.

2

x6

9.

x3

10. 8 y 5

Write your conclusions about radicals aftersolving the previous exercises. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________

4

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAMMATHEMATICS I

When simplifying a radical that does not have a perfect root, we break up or split the radicand into factors.

32 16 * 2 4 2
32 16 8 4 2 1

32
2 2 2 2 2

22  22 2 4 2
*Number of groups depends on the radical’s index. .

3
3 3

32 x 7 y 3 8 * 3 4 * 3 x7 y3
3

32 x 7 y 3
32 16 8 4 2 1 2 2 2 2 2

2x2 y

4x

3

23  x 6  y 3
3

3

22  x

2x2 y4x

* Number of groups depends on the radical’s index.

5

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

Determine the simplest expression.

1.

54

2.

3

320

3.

5 125

4.

10 200

5.

60a 2 b 7

6.

3

54a 2 b 3

6

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIASUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

7.

75 x 3 y 5

8.

27 4

9.

3

 40x 6

10.

4

162m 5 n 2

11.

32a 4 b6

7

UNIVERSIDAD DE MONTERREY
DIVISIÓN DE EDUCACIÓN MEDIA SUPERIOR ACADEMIA DE CIENCIAS EXACTAS

BICULTURAL PROGRAM MATHEMATICS I

12. 5a

3

16a 3b 6

13. 2 x 2 y

27 x 5 y 6

14. 5a

3

100a 3 b 6...