Worksheet 1

517 Basic radicals and the calculator Name:___________________

1.

16 = _______ 2.

81 = ________ 3.

121= __________

4.

! 64 = _________ 5.

! 144 = _________ 6.

0 = __________

7.

± 100 = _________ 8.

± 169 = __________ 9.

400 = ________

10. -

625 = ________ 11.

1

4 = ___________ 12.

!9

16 = _________

13.

±25

81 = ________ 14.

±49

100 = __________ 15.

±144

169= __________

16.

0.64 = _________ 17.

! 1.44 = __________18.

± 0.09 = __________

19.

! 0.01 = ________ 20.

± 0.0004 = ________ 21.

13 = __________

22.

!83 = __________ 23.

! !1253 = __________

Worksheet 2

517 Irrational numbers and simplification Name: ___________________

I. Circle all the irrational numbers below.

25

! 54

1

2

! 0.36

6.1504

40

! 150

1156

!4

9

0.1

2672.89

! 36

400

951

5.8044

II. Simplify.

1.

8 = __________ 2.

20 = ________ 3.

40 = _________

4.

27 = _________ 5.

54 = _________ 6.

90 = _________

7.

99 = _________ 8.

108 = _________ 9.

175 = _________

10.

4 12 = _________ 11.

4 90 = _________ 12.

3 200 = _________

Worksheet 3

517 Radical simplification with variables Name:____________________

Simplify the following radicals.

1.

4a2 = _________ 2.

16d2 = __________ 3.

49z2 = ___________

4.

16

25r2 = _________ 5.

0.81w2 = __________ 6.

9c2 = ___________

7.

36y4 = _________ 8.

c2d2 = __________ 9.

x4y2 = ___________

10.

r8s6 = _________ 11.

4x2y2 = __________ 12.

36a6b4 = ___________

13.

144a4b2 = ________ 14.

169x4y2 = __________ 15.

0.36m2 =

___________

Worksheet 4

517 Radical simplification with coefficients Name: ___________________

Simplify the following radicals.

1.

1

272 = _________ 2.

1

428 = __________ 3.

3

496 = ___________

4.

2

363= _________ 5.

5 24 = __________ 6.

2 80 = ___________

7.

7 45 = _________ 8.

8 9x = __________ 9.

3x3 = ___________

10.

x33 = _________ 11.

49x5 = __________ 12.

36r2s= ___________

13.

128x6 = _________ 14.

243xy2 = __________ 15.

720n7 = ___________

Worksheet 5

517 Radical addition and subtraction Name: ___________________

1.

8 2 ! 7 2 = __________ 2.

8 5 + 5 = _______________

3.

5 3 + 2 3 + 8 3 = _________ 4.

14 6 ! 2 6 = ______________

5.

7 2 ! 2 = ________________ 6.

4 3 + 2 3 ! 6 3 =____________

7.

15 y ! 7 y = ________________ 8.

2 + 50 = _______________

9.

27 + 75 = ____________ 10.

12 ! 48 + 3 = _____________

11.

5 27 ! 108 + 2 75 = ____________________

12.

6 16 ! 125 + 2 18= _____________________

Worksheet 6

517 Radical multiplication and division Name:____________________

1.

y( )2

= __________ 2.

3 6( )2

=_______________

3.

15x • 3x =_________ 4.

5x( )2

= ______________

5.

5 12( ) 4 3( ) = ________________ 6.

3 2( ) 2 32( ) =____________

7.

2

35

!

" #

$

% &

2

= ________________ 8.

9 6 ÷ 6 =_______________

9.

7 3 ÷ 3 3 = ____________ 10.

9y ÷ y = _____________

11.

12 20

3 5=_______________ 12.

20 50

4 2= _______________

13.

25 24

5 2 = ______________ 14.

3 54

6 3 = ____________________

Worksheet 7

517 Radicals mixed drill Name: ___________________

Perform the indicated operation and then simplify.

1. 2x + 5x = _____________

2.

2 7 + 5 7 = ________

3. 2x + 3y + 8x = _______________

4.

2 11 + 3 6 + 8 11 = ____________

5. 8x – x = __________

6.

8 3 ! 3 = ___________

7.

2 + 8 + 50 = __________

8.

12 + 24 ! 54 = __________

9. (

2 6 )2 = _________

10.

2 12 • 6= _________

11.

2 12 • 3 6 = _________

12. (

5 + 3)(

5 – 3) = __________

13. (x – 9)2 = ___________

ANSWER

14. Will lengths of 6.2 cm, 8.1cm and 4.3cm form a triangle? Justify your

answer.

15. Will lengths of

2 3 ft and 2 ft and

14 ft form a right triangle? Justify your

answer.

Worksheet 8

517 Radicals – Mixed practice with area Name: ___________________

Perform any indicated operation and leave the answer in simplified radical

form.

1.

75 = ________ 2.

4 28 = __________ 3.

2 5 ! 5 = ________

4.

(3 10)2 = ______ 5.

5 8 + 3 2 = _______ 6.

(2 12)• 4 = ________

7.

2 18 + 2 = __________ 8.

14 • 2= ____________

9.

2 3 • 3 2 = ______________ 10.

24 + 32 ! 54 = ___________

11.

2(5 + 3) = ____________ 12.

( 10 + 4)( 10 ! 4) = __________

13.

2 •5 3 = _____________ 14.

x3 = ____________

Worksheet 8 2

Find the area of the polygons below. Write answers as simplified radicals.

15. 16.

A = ________ A = ________

17. 18.

A = _______ A = ________

19. Rectangle ABCD has bases and altitudes that are 3 times the bases and

altitudes of rectangle PQRS. The area of rectangle ABCD is how many

times bigger than the area of rectangle PQRS?

______________

20.

Area = ________

6

2 3

8

4

2 5

4 2

6 2

2

2 6

Worksheet 9

517 Radical mixed practice Name:___________________

Express all irrational answers as simplified radicals.

1.

24 2.

40 3.

18 4.

72 5.

27

6.

3 28 7.

5 8 8.

2 80 9.

4 75 10.

7 x2

11.

7•2 3 12.

(4 44)• 3 13.

(2 50)• 4 14.

3•2 12

15.

3 • 6 16.

15 • 5 17.

8 • 8 18.

( 5)2

19.

3 8 • 3 20.

2 2 •5 10 21.

(3 5)2 22.

5 3 ! 3

23.

2 5 + 3 2 + 3 5 24.

4 + 2 6 + 3 25.

3 50 + 8

Worksheet 10

517 MCAS radical problems (2004-2006) Name:____________________

The following multiple-choice problems and short answer problems were on

the no-calculator section of previous MCAS tests. Use this assignment as an

opportunity to improve your ability to answer multiple-choice questions and

to analyze problems without a calculator.

1.

94 is best shown by what letter on the number line below?

W X Y Z 1. ________

8 9 10 11 12

2.

603 is best shown by what letter on the number line below?

W X Y Z 2. ________

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

3.

2 3 is between which two integers below? 3. ________

(A) 3 and 4 (B) 4 and 6 (C) 6 and 9 (D) 9 and 10

4. Which statement below is true? 4. ________

(A)

95 =10 (B)

95 >10 (C)

95 <10 (D)

95 < 9

5. Find the value of n in the expression

54

•5n

= 57 5. ________

6. Which statement is correct for the following list of numbers?

8

2

!2.3 0

2

7

9

.3

15

!12

! 6. ________

(A) There are 8 irrational numbers. (B) There are 7 irrational numbers.

(C) There are 3 irrational numbers. (D) There are 2 irrational numbers.

7. The expression

7 ! 2

2 is closest to which number below? 7. ________

(A) 1.1 (B) 2.8 (C) 6.3 (D) 6

Worksheet 10 2

8. Simplify the expression

24 ! (3+1)• 4

20 ! 24

8. ________

9. Which of the following statements is not true? 9. ________

(A)

121 is irrational. (B)

121 is an integer.

(C)

121 is a real number. (D)

121 is a rational number.

10. Which of the following is false for all positive values of n? 10. _______

(A)

n2

= n • n (B)

n2

= (n)• (!n) (C)

n2

= (!n)• (!n) (D)

n2

= n

11. Simplify

450 11. ________

(A)

15 2 (B)

45 2 (C)

75 2 (D)

225 2

12. Solve:

N =16 12. ________

13. Each statement that follows is true:

16n

= 4

9n

= 3

4n

= 2

What is the value of

3n? 13. ________

(A) 1 (B)

2 (C)

3 (D) 9