Chapter 4 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Identify the index of a.
. b.
7 c.
2 d.
3
____ 2. Identify the radicand of a.
8 b.
. c.
6 d.
4
____ 3. Order these numbers from greatest to least: a.
, , , , b.
, , , , c.
d.
, ,
,
____ 4. For which number will the fourth root be rational?
256, 27, –81, 40 000 a.
–81 b.
256 c.
40 000
,
,
,
,
____ 5. Which of these numbers is a whole number, but not a natural number?
0, –3, 1, a.
1 b.
c.
–3
,
,
, d.
27 d.
0
____ 6. Write a.
6 3
in simplest form. b.
____ 7. Write 6 5 as an entire radical. a. b.
____ 8. Write a.
as an entire radical. b.
____ 9. Write a.
as an entire radical. b. c.
c. c. c. d.
d. d. d.
____ 10. Order these numbers from greatest to least: a.
, , , , b.
, , , , c.
, d.
,
,
,
,
,
,
,
,
,
,
,
,
,
____ 11. Evaluate a.
b.
does not exist c.
d.

____ 12. Evaluate without using a calculator. a. b. c.
Short Answer
13. Evaluate .
14. Which of these numbers are irrational?
, , , 6.314, , –12.8, ,
15. Determine the edge length of a cube with volume 55 cm
3
.
Write your answer to the nearest tenth of a centimetre.
16. Write in simplest form.
17. Write 8 19 as an entire radical.
18. Write in simplest form.
19. Write as a radical.
d.
20. Evaluate without using a calculator.
21. Simplify
22. A sphere has volume 1417 cm . What is the radius of the sphere to the nearest tenth of a centimetre?
Problem
23. Is the cube root of 250 rational or irrational?
Use 2 different strategies to justify your answer.
24. A square has an area of 1134 m . Determine the perimeter of the square. Write the answer as a radical in simplest form.
25. In isosceles

ABC, what is the length of BC? Write your answer as a mixed radical.

A
10ft.
|
D
5 ft.
B C
26. Another 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 centimetre. b) Calculate the surface area of a person with height 170 cm and mass 66 kg. Write the decimal to the nearest hundredth of a square centimetre.
, answer as a
27. Here is Tanisha’s solution for evaluating a power:
Identify the errors Tanisha made. Write a correct solution.
28. Koli wants to invest enough money on January 1st to pay his daughter $900 at the end of each year for the next 6 years.
The investment savings account pays 3.3% compounded annually.
The amount, A dollars, that Koli must invest on January 1st is given by the formula:
, where P is the annual payment in dollars, r is the annual interest rate expressed as a decimal, and t is the time in years that the money will be invested.
How much must Koli invest on January 1st?
29. A colony of bacteria start with 100 bacteria. The population of the colony doubles each every 20 min. This equation represents the population, N bacteria, after t hours:
How would the population after min compare with the population after 105 min?
Write your answer as a percent.
30. A cone with equal height and radius has volume 492 cm
3
. What is the height of the cone to the nearest tenth of a centimetre?
31. Identify any errors in each simplification. Write a correct solution. a)

b)
32. Use exponent laws to simplify . Explain your strategy.

Chapter 4 Review
Answer Section
MULTIPLE CHOICE
1. ANS: D
LOC: 10.AN2
2. ANS: B
LOC: 10.AN2
3. ANS: B
LOC: 10.AN2
4. ANS: B
LOC: 10.AN2
5. ANS: D
LOC: 10.AN2
6. ANS: A
LOC: 10.AN2
PTS: 1 DIF: Easy
TOP: Algebra and Number
PTS: 1
PTS: 1
PTS: 1
DIF: Easy
TOP: Algebra and Number
DIF: Moderate
TOP: Algebra and Number
DIF: Moderate
TOP: Algebra and Number
PTS: 1 DIF: Easy
TOP: Algebra and Number
PTS: 1 DIF: Easy
TOP: Algebra and Number
REF: 4.1 Estimating Roots
KEY: Procedural Knowledge
REF: 4.1 Estimating Roots
KEY: Procedural Knowledge
REF: 4.2 Irrational Numbers
KEY: Conceptual Understanding
REF: 4.2 Irrational Numbers
KEY: Conceptual Understanding
REF: 4.2 Irrational Numbers
KEY: Procedural Knowledge
REF: 4.3 Mixed and Entire Radicals
KEY: Conceptual Understanding
7. ANS: D
LOC: 10.AN2
8. ANS: C
LOC: 10.AN2
PTS: 1 DIF: Easy
TOP: Algebra and Number
PTS: 1 DIF: Easy
TOP: Algebra and Number
REF: 4.3 Mixed and Entire Radicals
KEY: Conceptual Understanding
REF: 4.3 Mixed and Entire Radicals
KEY: Conceptual Understanding
9. ANS: B
LOC: 10.AN2
10. ANS: B
LOC: 10.AN2
PTS: 1 DIF: Easy
TOP: Algebra and Number
PTS: 1 DIF: Moderate
TOP: Algebra and Number
REF: 4.3 Mixed and Entire Radicals
KEY: Conceptual Understanding
REF: 4.3 Mixed and Entire Radicals
KEY: Conceptual Understanding
11. ANS: C PTS: 1 DIF: Moderate
REF: 4.4 Fractional Exponents and Radicals
TOP: Algebra and Number
LOC: 10.AN3
KEY: Conceptual Understanding
12. ANS: D PTS: 1 DIF: Moderate
REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number
LOC: 10.AN3
KEY: Conceptual Understanding
SHORT ANSWER
13. ANS:
PTS: 1
LOC: 10.AN1
14. ANS:
,
PTS: 1
, and
LOC: 10.AN2
15. ANS:
3.8 cm
DIF: Easy REF: 4.1 Estimating Roots
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Easy REF: 4.2 Irrational Numbers
TOP: Algebra and Number KEY: Conceptual Understanding

PTS: 1
LOC: 10.AN1
16. ANS:
11 14
PTS: 1
LOC: 10.AN2
17. ANS:
PTS: 1
LOC: 10.AN2
18. ANS:
PTS: 1
LOC: 10.AN2
19. ANS:
or
PTS: 1
LOC: 10.AN3
20. ANS:
9
4
PTS: 1
LOC: 10.AN3
21. ANS:
DIF: Easy REF: 4.2 Irrational Numbers
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Easy REF: 4.3 Mixed and Entire Radicals
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Easy REF: 4.3 Mixed and Entire Radicals
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Moderate REF: 4.3 Mixed and Entire Radicals
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Easy REF: 4.4 Fractional Exponents and Radicals
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Moderate REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
22. ANS:
cm
PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number KEY: Conceptual Understanding
DIF: Moderate REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number KEY: Conceptual Understanding
PROBLEM
23. ANS:
250 is not a perfect cube, so the cube root of 250 is irrational.
=

So, the cube root of 250 is likely irrational.
PTS: 1
LOC: 10.AN1
DIF: Moderate REF: 4.2 Irrational Numbers
TOP: Algebra and Number KEY: Problem-Solving Skills
24. ANS:
The formula for the area, A, of a square is , where s is the side length of the square.
As a mixed radical in simplest form:
The formula for the perimeter, P , of a square is .
The perimeter of the square is
PTS: 1
LOC: 10.AN2
m.
DIF: Moderate REF: 4.3 Mixed and Entire Radicals
TOP: Algebra and Number KEY: Problem-Solving Skills
25. ANS:
Use the Pythagorean Theorem in

ABD to determine BD.
So,
The length of BC is
PTS: 1
LOC: 10.AN2
26. ANS:
ft.
DIF: Moderate REF: 4.3 Mixed and Entire Radicals
TOP: Algebra and Number KEY: Problem-Solving Skills
Use the formula: a) Substitute: h = 48 and m = 7.3

Use a calculator.
The surface area of a newborn with height cm and mass 7.3 kg is approximately 0.32 cm . b) Substitute: h = 170 and m = 66

Use a calculator.

The surface area of a person with height 170 cm and mass 66 kg is approximately 1.58 cm .
PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.4 Fractional Exponents and Radicals
TOP: Algebra and Number KEY: Problem-Solving Skills
27. ANS:
Tanisha made an error in the first line when she wrote the square root symbol ( ) instead of the ( ) symbol. Also, the exponent outside the bracket should have been 2, not 7. (The numerator of a fractional exponent represents the index of the radical and the denominator represents the exponent of the power.)
A correct solution:
PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.4 Fractional Exponents and Radicals
TOP: Algebra and Number
KEY: Problem-Solving Skills | Communication
28. ANS:
Use the formula. Substitute: P = 900, r = 0.033, t = 6

Koli should invest $4827.36 on January 1st.
PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number KEY: Problem-Solving Skills
29. ANS:
Use the equation:
Substitute: t = 60 Substitute: t = 105
To compare the populations after min and after 105 min, divide:
Write 0.210 as a percent: %
The population after min would be approximately 21.0 % of the population after 105 min.
PTS: 1
LOC: 10.AN3
DIF: Difficult REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number KEY: Problem-Solving Skills
30. ANS:
The volume of a cone with base radius r and height h is given by the formula:
The cone has equal height and radius.
So, substitute: r = h

Substitute V = 492, then solve for h .
Multiply each side by 3.
Divide each side by

.
To solve for h , take the cube root of each side by raising each side to the one-third power.
Use a calculator.
The height of the cone is approximately 7.8 cm.
PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number KEY: Problem-Solving Skills
31. ANS: a) There is an error in the second line. When multiplying powers with the same base, the exponents should have been added, not multiplied.
A correct solution: b) There are two errors in the first line. The coefficient 2 was incorrectly multiplied by the exponent –4.
And, the exponent of the variable n was added to –4 instead of being multiplied by –4.
A correct solution:

PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number
KEY: Problem-Solving Skills | Communication
32. ANS:
Write each radical as a power.
Use the product of powers law:
Write equivalent fractions with a common denominator, 40.
I can write this power as a radical:
or
PTS: 1
LOC: 10.AN3
DIF: Moderate REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number
KEY: Problem-Solving Skills | Communication