Radicals Grade 9october 29

Grade 9

October 29, 2009 Worksheet Radicals

I- Simplify: 1) 4)

2)

81 + 25

(

2− 3

)

3) 3 2 ( 2 −5)

5 5 + 80 − 45

5) (5 2 + 2 )(1 − 2 )

3

6)

12 + 27

II- Calculate: 1) x 2 + y 2

for x = 3 2 and

y= 6

for

x= 8

and

y = 50

3) xy

for

x= 3

and

y =2 6

4) x 2

for

x =2 + 3

2)

III-

( x + y) 2

Given the following numbers:

a = 2 63 + 28 − 175

;

(

)(

b = 3 − 5 3 5 +5

);

c = 2 7 × 33 × 5 4

Simplify a, b, and c.

IV-Simplify: 1)

7 2 − 33

8)

50 + 72 − 4 8

2)

7 2 − 32

9)

7 × 14 × 2 × 11

3)

(− 4 + 2 3 )

4)

27 10 × 5 3

3

10)

2 49 + 5 4 3 16

11) (3 2 )2 − (− 2 3 ) 2

5)

2 7 14 + 3 2

12) 9 2 + 3 2 − 9 + 10

6) (1 + 5 )(2 + 5 ) 7)

2 4 × 24

(

)

V- Given x = 2 1 + 6 and y = 2 − 6

Calculate x 2 ; y 2 and x 2 + y 2

VI- Given A=

15

(

) and B=

80 −1

(

3 20 − 5

)

Show that A = B

VII-

Let a = 2 12 and

b = −3 3

Calculate: a = b

ab =

b2 =

3 6

VIII-

Can you write the number

5 4 2

without a radical? Show your work.

7 15

IX- Let E =

48 + 20

and F =

108 − 45

a) Simplify E and F b) Verify that E × F is a natural number

X- Given the following expressions: A=

5+ 5

B=

500 5

C= E=

2 5

5

D=

20

5 +5

Show that three of these numbers are equal

XI-The unit of length is centimeter Given a rectangle of dimensions

x = 4 +2 3

and

y =8 + 3

1) Identify the length and the width of the rectangle 2) Express the area of this rectangle in the form of a +b 3 where

a and

b are

integers 3) Compare the area of this rectangle to the area of the square of side 5 +2 3