Which of the following are irrational numbers? *
10 points
3√8
√25
3√2 x √8
√12
Other:
Answers
Answer:
Irrational Numbers
Are there any decimals that do not stop or repeat? Yes. The number
π
(the Greek letter pi, pronounced ‘pie’), which is very important in describing circles, has a decimal form that does not stop or repeat.
π
=
3.141592654…….
Similarly, the decimal representations of square roots of numbers that are not perfect squares never stop and never repeat. For example,
√
5
=
2.236067978…..
A decimal that does not stop and does not repeat cannot be written as the ratio of integers. We call this kind of number an irrational number.
IRRATIONAL NUMBER
An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
Let’s summarize a method we can use to determine whether a number is rational or irrational.
If the decimal form of a number
stops or repeats, the number is rational.
does not stop and does not repeat, the number is irrational.
EXAMPLE
Identify each of the following as rational or irrational:
1.
0.58
¯¯¯
3
2.
0.475
3.
3.605551275
…
Show Solution
Solution:
1.
0.58
¯¯¯
3
The bar above the
3
indicates that it repeats. Therefore,
0.58
¯¯¯
3
is a repeating decimal, and is therefore a rational number.
2.
0.475
This decimal stops after the
5
, so it is a rational number.
3.
3.605551275
…
The ellipsis
(
…
)
means that this number does not stop. There is no repeating pattern of digits. Since the number doesn’t stop and doesn’t repeat, it is irrational.
Step-by-step explanation:
In this chapter, we’ll make sure your skills are firmly set. We’ll take another look at the kinds of numbers we have worked with in all previous chapters. We’ll work with properties of numbers that will help you improve your number sense. And we’ll practice using them in ways that we’ll use when we solve equations and complete other procedures in algebra.
We have already described numbers as counting numbers, whole numbers, and integers. Do you remember what the difference is among these types of numbers?
counting numbers
1
,
2
,
3
,
4
…
whole numbers
0
,
1
,
2
,
3
,
4
…
integers
⋯
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3
,
4