Which of the following is irrational 3.6363636363.. 52.781654292 √3/4 - 7 8/37
To determine which of the numbers is irrational, let's check the definition of an irrational number.
An irrational number is a number that cannot be represented as a fraction p/q, where p and q are integers and q is not zero.
Now let's analyze the given numbers:
1. 3.6363636363...
This number can be expressed as a fraction. It is a repeating decimal, and when written in fraction form, it evaluates to 40/11. Therefore, it is rational.
2. 52.781654292
This number is a finite decimal. It is not repeating, and it can be expressed as a fraction with a denominator of 1. Therefore, it is rational.
3. √3/4 - 7
√3/4 is the square root of 3 divided by 4. This is an irrational number because the square root of 3 cannot be expressed as a fraction. Subtracting 7 from an irrational number does not change its nature, so the entire expression is also irrational.
4. 8/37
This number is a fraction where both the numerator and denominator are integers. Therefore, it is rational.
Based on the analysis, the irrational numbers are √3/4 - 7.