Which of the following is irrational?
-7 8/37
52.781654292
√3/4
3.6363636363636363
√3/4 is irrational.
To determine which of the following numbers is irrational, we need to assess whether each number is a rational number or not.
A rational number can be expressed as a fraction of two integers, whereas an irrational number cannot be expressed as a fraction and has an infinite non-repetitive decimal expansion.
Let's evaluate each option:
-7 8/37: This is a mixed number, which can be expressed as a rational number. Therefore, it is not irrational.
52.781654292: This is a decimal number. However, decimal numbers can still be rational if they can be expressed as a fraction. Since we don't have any further information about this number, we cannot determine if it is rational or irrational.
√3/4: This is an example of a radical expression (√). The square root of 3 (√3) cannot be expressed as a simple fraction, so it is considered an irrational number. Therefore, this option is irrational.
3.6363636363636363: This is a decimal number that has a repeating decimal pattern, indicated by the repeating digit "3". Repeating decimals can be expressed as fractions and are therefore rational. Therefore, this option is not irrational.
Based on this analysis, the only option that is definitely irrational is √3/4.