Which of the following is irrational?
-√25
√16/25
0.010011000111
√2
π
π
There are others:
√2 is irrational
if for 0.010011000111 you meant 0.010011000111.....
it would be irrational, since according to the pattern shown, the
decimals would never repeat in a defined pattern.
To determine which of the following numbers is irrational, we need to understand what it means for a number to be irrational.
A number is considered irrational if it cannot be expressed as the ratio of two integers (i.e., it cannot be written as a fraction).
Now let's evaluate each of the given numbers:
-√25:
-√25 is equal to -5, which can be expressed as the ratio -5/1. Therefore, -√25 is not irrational.
√16/25:
√16/25 can be simplified to √16 / √25. √16 equals 4 and √25 equals 5, so we have 4/5. 4/5 can be expressed as the ratio of two integers (4 and 5). Therefore, √16/25 is not irrational.
0.010011000111:
0.010011000111 is a decimal representation of a number. It appears to be a non-repeating decimal, but to determine if it's rational or irrational, we would need more information about the pattern to confirm. The given number alone does not provide enough information to determine if it is rational or irrational.
√2:
√2 is an example of an irrational number. It cannot be expressed as the ratio of two integers and it is a non-repeating decimal. Therefore, √2 is irrational.
π (Pi):
π is also an example of an irrational number. It cannot be expressed as the ratio of two integers and it is also a non-repeating decimal. Therefore, π is irrational.
In summary, the two numbers that are irrational from the given options are √2 and π.
To determine which of the given options is irrational, we need to understand what an irrational number is. An irrational number is a real number that cannot be expressed as a fraction or ratio of two integers.
Now let's analyze each option:
-√25: This is equal to -5. Since -5 can be expressed as the ratio -5/1, -√25 is rational.
√16/25: Simplifying the numerator and denominator, we get √16/√25 = 4/5. This is a ratio of two integers, so √16/25 is rational.
0.010011000111: This is a decimal number. Although it might not seem like an obvious fraction, we need to check if it can be written as a ratio of two integers. By converting the decimal to a fraction, we find that 0.010011000111 = 900/89991. Therefore, 0.010011000111 is rational.
√2: The square root of 2 (√2) is an irrational number. It cannot be expressed as a fraction or ratio of two integers. This is the only option that is irrational.
π: Pi (π) is also an irrational number. It is the ratio of a circle's circumference to its diameter and cannot be expressed exactly as a fraction or ratio of two integers.
So, the irrational numbers among the given options are √2 and π.