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Math 10C Roots and Powers
1. Qui-Gon Jinn is strong in the ways of number systems. He has made four
statements below.
I.
II.
III.
IV.
1331 is a natural number.
All rational numbers are real numbers.
Rational numbers include non-terminating decimals.
All whole numbers are natural numbers.
3
Which of the above statements are TRUE?
a) I & II only b) I, II & IV only c) I, II & III only d)All of the statements are correct.
2. Identify the index of
a. 83
b.4
4
83
c.8
d. 3
3. Identify the radicand of 34
a. 2
b. 34 c.3
d. 4
4. The Area A, in squared centimeters of each cube is given. For which is the edge length,
s, a rational number? A  s 2
a) A = 30 cm2
b) A = 75 cm2
c) A = 64 cm2
d) A = 150 cm2
5. Which of these numbers is irrational?
,
,
,
a.
b.
c.
6. Order these numbers from least to greatest:
a.
,
c.
,
,
,
,
,
,
,
b.
d.
,
d.
,
,
,
,
,
,
,
,
,
,
,
7. Between which two consecutive integers on a number line would you locate
a. -2 and -3
b. -3 and -4 c. 2 and 3
d.-1 and -2
1
?
Math 10C Roots and Powers
8. Which of these numbers is a natural number?
9, 0, –1,
a. 0
b. 9
c. -1
9. Write
d.
in simplest form.
a.
10. Write
b.
c.
d.
c.
d.
c.
d.
c.
d.
in simplest form.
a.
b. 7 2
11. Write 7 14 as an entire radical.
a.
b.
12. Write
as an entire radical.
a.
b.
13. A cube has a volume of 7290 cm . Determine the edge length of the cube as a radical in
simplest form.
a.
cm
b.
cm
c.
cm
d.
cm
14. Write
as a power.
a.
15. Write
b.
c.
d.
as a radical.
a.
, or
, or
, or
c.
d.
16. Evaluate
a.
, or
b.
without using a calculator.
1
256
3
256
b.
1
256
c.
-
2
d.
–256
Math 10C Roots and Powers
17. Paleontologists use measurements from fossilized dinosaur tracks and the formula
to estimate the speed at which a dinosaur travelled.
In the formula, v is the speed in metres per second, s is the distance between successive
footprints of the same foot, and f is the foot length in metres.
Estimate the speed of the dinosaur when the distance between footprints, s, is 1 m and
the foot length, f, is 0.65 m.
a. About 0.09 m/s
b. About 0.43 m/s
c. About 0.07 m/s
d. About 0.26 m/s
18. Simplify
a.
. Write using powers with positive exponents.
b.
d.
c.
2
 5 7
19. A student simplified   as followed:
4
Line 1
Line 2
Line 3
Which line did the student make a mistake?
a. Line 1
20. Simplify
a. 3.51
b. Line 2
d. There are no mistakes
by writing as a single power.
b. 3.5-29
21. Simplify
a.
c. Line 3
c. 3.50
d. 3.5-2
.
b.
d.
c.
3
Math 10C Roots and Powers
22. Simplify
c.
b.
d.
c.
23. Simplify
a.
c.
b.
d.
Part B: Numerical Response
1.
To the nearest hundredth, determine the value of
5
36
1
42  4 2
2.
Determine the value of
to the nearest whole number.
44
3.
The intensity of light at its source is 100%. The intensity, I, at a distance d centimetres
from the source is given by the formula
. Use the formula to determine the
intensity of the light 25 cm from the source. Round your answer to the nearest hundredth.
Part C: Written Response
1. A formula for the approximate surface area, SA square metres, of a person’s body is
, where h is the person’s height in centimetres, and m is the person’s mass
in kilograms.
a) Calculate the surface area of a newborn with height cm and mass 7.3 kg. Write the
answer as a decimal to the nearest hundredth of a square metre.
b) Calculate the surface area of a person with height 170 cm and mass 66 kg. Write the
answer as a decimal to the nearest hundredth of a square metre.
2. Order these numbers from least to greatest:
3. Simplify the following: [3 marks]
7 3  3 3 =______________________
a.
b.
c.
8  18  32 =______________________
3 20  45  7 5 =_______________________
4
,
,
,
,
Math 10C Roots and Powers
ANSWERS
Part A Multiple Choice:
1. A
2. B
3. B
4. C
Only perfect square is 64
5. A
48  6.92820...
15. D
Calculator Keys:
0.155(1)  (5 / 3)  (0.65)  (7 / 6)
= 0.256212
= 0.26 m/s
16. D
12 p3q 7 4 31 76 4 2 13 4 p 2
 p q
 p q  13
15 pq6
5
5
5q
17. A
216  6
3
49 9

16 4
68
4. B
3
75 4.21716
14
3
3.74166
100
4.64159
17
4.12311
30
3.10723
3
2
19. A
11 7
7  11  5 7
4 2


 74  53 

  
4 3
4  4 3 3
4 3
7
s
t

6
s
t


42
s
t


42
s
t






5. A
3
2
18
42t 3
 42s t 
s
2
1 3
2.62074
6. B
7. B
3
2
 5 7  7 5 

   
 4   4 
18. C
3.56 3.55   3.565  3.51  3.511  3.50
3.51
3.51
3.51
20. B
80  3 8 10  2 3 10
m n 
 m n
3 3 1
8. B
98  49  2  7 2
2
9. C
7 14  72 14  49 14  686
10. B
21. D
 w15 y12 

3 
 64 x 
16 3  16  3  4096  3  12288
11. B
3
7290  3 729 10  9 3 10
12. B
13. D
3
3
3
3
3
 7.5 4  4 7.55 or  4 7.5 
5

4
3

1
 64
4
3
1

3
64
4
5


1
3
1
1
1

4
4
256
5
1
 64 x3  3  64  3 x1
4 x
4w5 x
  15 12  


w5 y 4
w5 y 4
y4
w y 
Part B Numerical Response:
1. 2.05
5
36  2.04767... = 2.05
2. 528
Calculator:
(4  2  4  (1/ 2)) / 4  4
3. 0.16
100(25)2  0.16
14. A
 64 
4
m3n3
m5
3 ( 8) 3 4
5 1
 8 4  m
n m n 
m n
n
Math 10C Roots and Powers
Part C Written Response
1. a)
2
1
SA  0.025(48) 5 (7.3) 2
 0.317759 m 2
 0.32 m 2
b)
2
1
SA  0.025(170) 5 (66) 2
 1.584497 m2
 1.58 m2
13 3
, 128, 38, 3 515
3
38 6.16
2,
2.
3
515
8.02
13
 4.3
3
2 1.41
3
3.
4.
128
5.04
a. 7 3  3 3  10 3
8  18  32 = 4  2  9  2  16  2  2 2  3 2  4 2  3 2
b.
c. 3 20  45  7 5  3 4  5  9  5  7 5  6 5  3 5  7 5  2 5
Check-off the number sets each of the following numbers belongs to. [2 mark]
N
W
I
Q
R
Q
3
 64
1
X
X
X
X
X
X
X
X
X
X
5
7
2.565665666…
5.
X
Simplify the following. Answers must contain positive exponents only.
a. (2x5)(3x4) = 6x9
2
b. (2x2y4) = 2 4
x y
2
c.
2
2
 15x 4 
25
=  5x 47    5x 3   25x 6  6

7 
x
 3x 
6
X
Math 10C Roots and Powers
 5x
d.
2
y3  
2
5x
1
2
y3 
2
1
x4

25x 4 y6 25y6

e. a 8  a 5 = a 85  a 3
8c5 d 2   3cd  24c 6 d 3 3 62 32 3 4

3c 4 d
f.
or


c
d

c
d
2
16c 2 d 2
16c 2 d 2 2
2
4 8
2
9y z
g.  3x 3 y 2 z 4   (3)2 x 6 y 4 z 8 
x6
6x 5
2
h.
 2x 57  2x 2   2
7
3x
x
3
3
4
 4 a 2  4 1 a 2  4(1 a 6 )  4a 6
i.

3
a 2
  
 
 2x y  6xy   12x y
4
j.
9
3

5 12
9 14
 3x 59 y1214  3x 4 y2 
9 14
4x y
4x y
90  9 10  3 10
b.
320  3 64  5  4 3 5
6.
a.
7.
a. 7 6  72  6  49  6  294
8.
a. 17 5  5 179 or
9.
a.
10.
  
9
8
x x
y
x
5
y
2
 
b.
1
5
5 2  53 or
b.
15  15
7
3
b. 113 4  3 113  4  3 1331 4  3 5324
3
9
17
5
3
1 3

5
x3  x 8  x 5  x 8
 5
3
7
5
5
 x 40
3
x y2
4

24
40
29
 x 40  40 x 29
7