Which of the following is irrational?(1 point)
Responses
3.6363636363636363...
3.6363636363636363...
3√4
Start Fraction Start Root 3 End Root over 4 End Fraction
−7837
negative 7 Start Fraction 8 over 37 End Fraction
52.781654292
The irrational numbers in the given options are:
1. 3√4 (since the square root of 4 is not a whole number)
2. Start Fraction Start Root 3 End Root over 4 End Fraction (since the square root of 3 divided by 4 is not a whole number)
Therefore, option 3.6363636363636363... and 52.781654292 are rational numbers since they can be expressed as fractions or terminating decimals.
To determine which of the following numbers is irrational, we need to recall the definition of an irrational number. An irrational number is a number that cannot be expressed as a fraction (or ratio) of two integers and also cannot be expressed as a terminating or repeating decimal.
Let's go through each option:
1. 3.6363636363636363...
This number is a repeating decimal, with the repeating pattern of 36. Thus, it can be expressed as a fraction, making it a rational number.
2. √3/4
This number is the square root of 3 divided by 4. The square root of 3 is an irrational number, and dividing it by 4 does not change its irrationality. So, √3/4 is an irrational number.
3. -7837
This is a whole number and can be expressed as the fraction -7837/1, making it a rational number.
4. -7 8/37
This is a mixed number, which can also be expressed as a fraction. Therefore, it is a rational number.
5. 52.781654292
This number is a decimal, but it is not a repeating or terminating decimal. However, without additional information, we cannot determine if this number is irrational or rational.
Based on the given options, the only number that is definitely irrational is √3/4.