Which of the following sets are irrational numbers
U forgot the sets
Which of the following numbers is an irrational number? *
(a) 16−√ 4
(b) (3 – √3) (3 + √3)
(c) √5 + 3
d) -√25
To determine which sets of numbers are irrational, we need to understand what it means for a number to be irrational. An irrational number is any real number that cannot be expressed as a fraction (ratio) of two integers. In other words, it is a number that cannot be written in the form a/b, where a and b are integers and b is not equal to zero.
Now, let's consider the following sets of numbers and determine if they are irrational:
1. {π, √2, e}:
- π (pi) is irrational. It is a transcendental number and cannot be expressed exactly as a finite fraction or a repeating decimal.
- √2 (square root of 2) is also irrational. It cannot be written as a simple fraction because it is an irrational square root.
- e (Euler's number) is irrational as well. It is a transcendental number and cannot be represented as a fraction.
Therefore, in set {π, √2, e}, all the numbers are irrational.
2. {7, -3, 0}:
- 7, -3, and 0 are all rational numbers because they can be expressed as fractions of integers. For example, 7 can be written as 7/1, -3 as -3/1, and 0 as 0/1.
Therefore, in set {7, -3, 0}, all the numbers are rational.
3. {√9, 2/5, -11}:
- √9 (square root of 9) is rational. It equals 3 because 3/1 is a simple fraction representation of 3.
- 2/5 is also a rational number because it can be expressed as a fraction.
- -11 is a rational number, as it can be written as -11/1.
Therefore, in set {√9, 2/5, -11}, all the numbers are rational.
To summarize, the set containing π, √2, and e is the only set where all the numbers are irrational.