517 Radicals Packet
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Transcript of 517 Radicals Packet
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