Question

Which of the following is an irrational number?

A. 0.333

B. \sqrt{8}

C. \sqrt{49}

D. 5 over 22

Answer 1

To determine which of the options is an irrational number, let's analyze each one:

A. \( 0.333 \) - This is a repeating decimal, which can be expressed as the fraction \( \frac{1}{3} \). This means it is a rational number.

B. \( \sqrt{8} \) - This can be simplified to \( \sqrt{4 \cdot 2} = 2\sqrt{2} \). Since \( \sqrt{2} \) is an irrational number, \( \sqrt{8} \) is also irrational.

C. \( \sqrt{49} \) - This is equal to \( 7 \), which is an integer and thus a rational number.

D. \( \frac{5}{22} \) - This is a fraction where both the numerator and denominator are integers, so it is a rational number.

The only irrational number among the options is:

**B. \( \sqrt{8} \)**.