Math 10
Unit 4 Roots and Powers
Assignment
Name:________________________
4.2:
1. Tell whether each number is rational or irrational.
2. Classify each number below as:
a) a natural number,
b) an integer,
3. a) Why are
b) Why are
c) a rational number,
49 and
4
16 rational numbers?
21 and
3
36 irrational numbers?
d) an irrational number.
Because their decimal forms do not terminate, nor repeat in a pattern.
4. Look at this calculator screen.
a) Is the number 12.247 448 71 rational or
irrational? Explain.
b) Is the number
150 rational or irrational? Explain.
is an irrational number because
150 = 5 ⋅ 5 ⋅ 2 ⋅ 3 = 5 2 ⋅ 3
5. a) Sketch a diagram to represent the set of rational numbers and the set of irrational numbers.
b)Write each number that follows in the correct set.
6. For which numbers will the cube root be irrational? Show how to justify your answers.
a)
c)
8
b)
30
d)
64
300
7. Sketch a number line for each irrational number and label its approximate location.
8. a) Which of the following statements are true?
i) All natural numbers are integers.
____________
ii) All integers are rational numbers.
____________
iii) All whole numbers are natural numbers.
____________
iv) All irrational numbers are roots.
____________
v) Some rational numbers are natural numbers.
____________
b) For each statement in part a that is false, provide examples to explain why.
9. Write a number that is:
a) a rational number but not an integer
b) a whole number but not a natural number
c) an irrational number
10. Determine whether the perimeter of each square is a rational number or an irrational number.
Justify your answer.
a) a square with area 40 cm2
b) a square with area 81 m2
11. This diagram shows a cube with volume V cubic units and edge length s units.
Provide a value of V for which s is:
a) irrational
b) rational