Copyright © Swun Math Grade 8 Unit 1 Lesson 3 P TEStudent Practice
Unit 1 · Lesson 3: Rational vs. Irrational Numbers
Directions: Read and solve. Justify your answer.
- Is √ 9 a rational number?
Solution:
Yes
We know that 9 is equal to 3 times 3. This makes the
equation read: √ 3 ⋅ 3
9 is equal to 3 which is an integer. All integers are rational.
Since 3 is the same as writing 3
1, and both 3 and 1 are
integers, then yes, this is a rational number.- Is 7,892,564 a rational number?
Solution:
Yes
This is a big and complex looking number, but it is still an
integer and integers are rational numbers.
Since it can be rewritten as 7892564/1, and both 7892564
and 1 are integers, then yes, it is a rational number.
Is (^) √ 79 rational number?
Solution:
No
Examine 79, it is not a perfect square number under the
radical.
Square roots of perfect squares are classified as rational
numbers because they are integers.
Is 9.2 a rational number?
Solution:
Yes
The number 9.2 can easily be converted to fraction form by
making it 92
10.Since both 92 and 10 are integers, then this is a rational
number.
Since 9.2 is a terminating decimal, it is called a rational
number.- Which of the following is/are rational
numbers? Justify your answer.
a. 2.5
b. (^) √ 2
c. (^) √ 81
d. 29.5826593...
Solution:
(a) because 2.5 can be written as a fraction
(c) 81 is a perfect square; 81 = 9 and 9 can be written as a
ratio in the form of^9
1
.
- Which of the following is/are irrational
numbers? Justify your answer.
a. (^) √ 7
b. 1.973258...
c. 10.5
d.
1
3
Solution:
(a) because seven is not a perfect square
(b) since it is a non-terminating decimal that lacks and
cannot be written in a fraction from.
Name:
Date: