Question

Which of the following is irrational?
options:

3.6363636363636363...

3√ over 4

−7 and 8 over 37

52.781654292

Answer 1

To determine which of the given options is irrational, let's analyze each option:

1. **3.6363636363636363...**: This number is a repeating decimal (the "63" repeats indefinitely), which can be expressed as a fraction. Any repeating decimal is rational. Therefore, this number is rational.

2. **3√ over 4 (or \(\sqrt[3]{4}\))**: The cube root of a rational number (like 4) is also rational. Therefore, \(\sqrt[3]{4}\) is rational.

3. **−7 and 8 over 37 (or \(-7 + \frac{8}{37}\))**: The expression can be simplified as a fraction after doing the arithmetic. Since it is a simple arithmetic operation involving whole numbers and a fraction, it is rational.

4. **52.781654292**: This is a decimal that terminates and can be expressed as a fraction. Therefore, it is rational.

Among all the options, none of them are irrational. However, if you're looking for irrational numbers, it's important to know examples like \(\pi\), \(\sqrt{2}\), and other non-repeating, non-terminating decimals.

Thus, none of the given options are irrational.