Question

Which of the following is irrational?

options:

3.6363636363636363...

3√4

−7 and 8 over 37

52.781654292

Answer 1

To determine which of the options is irrational, let’s analyze each one:

1. **3.6363636363636363...**: This number can be expressed as the fraction \( \frac{363636...}{100000...} \). This is a repeating decimal, which is equivalent to the fraction \( \frac{11}{3} \). Therefore, it is rational.

2. **3√4**: This represents \( \sqrt[3]{4} \). The cube root of 4 cannot be expressed as a fraction of two integers, and therefore it is an irrational number.

3. **−7 and 8 over 37**: This seems to be a misinterpretation; likely it refers to \( -7 + \frac{8}{37} \). Both \(-7\) and \(\frac{8}{37}\) are rational numbers, and the sum of two rational numbers is also rational. Thus, this option is rational.

4. **52.781654292**: This is a finite decimal and can be expressed as a fraction, so it is rational.

Based on the analysis:

The irrational number among the options is \( 3\sqrt{4} \).