which of the following is an irrational number?
4pi/pi
v30
7.222…
33/v25
v30
An irrational number is a number that cannot be expressed as a simple fraction or a decimal that terminates or repeats.
Out of the four options you provided:
1. 4π/π simplifies to 4, which is a rational number.
2. √30 is irrational because it cannot be expressed as a fraction or decimal that terminates or repeats.
3. 7.222... is a decimal representation, but without further information, we cannot determine if it is rational or irrational. If the decimal representation repeats or terminates, it is rational; otherwise, it is irrational.
4. 33/√25 simplifies to 33/5, which is a rational number.
Therefore, the correct answer is √30, option (b), which is an irrational number.
To determine which of the following numbers is an irrational number, we need to understand what an irrational number is. An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. It is a non-repeating and non-terminating decimal.
Let's analyze each option:
1. 4π/π:
We can simplify this expression by canceling out the πs. The result is 4, which is a rational number since it can be expressed as 4/1. Therefore, 4pi/pi is not an irrational number.
2. √30:
To determine if √30 is irrational, we need to find its square root. If the square root of 30 is a non-repeating and non-terminating decimal, then it is an irrational number. Using a calculator, we find that the square root of 30 is approximately 5.47722557505. Since this number does not repeat, it is an irrational number.
3. 7.222...:
This number is given as a decimal and does not have an explicit pattern mentioned. However, since it does not repeat or terminate, we can conclude that it is an irrational number.
4. 33/√25:
We can simplify this expression by calculating the square root of 25, which is 5. After simplification, we have 33 divided by 5, resulting in a decimal value of 6.6. Since this decimal has a repeating pattern and is terminating, it is a rational number.
Therefore, the irrational number among the given options is √30.