Questions: Which one of the following is a rational number? (A) sqrt(2)/2 (C) 3/sqrt(5)

Solution Steps

To determine which of the given options is a rational number, we need to check if the number can be expressed as a ratio of two integers. A rational number is any number that can be written as a fraction where both the numerator and the denominator are integers.

A rational number is any number that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).

Option A is \(\frac{\sqrt{2}}{2}\).

• Calculate \(\sqrt{2}\): \[ \sqrt{2} \approx 1.4142 \]
• Therefore, \(\frac{\sqrt{2}}{2} \approx \frac{1.4142}{2} \approx 0.7071\).

Since \(0.7071\) cannot be expressed as a ratio of two integers, \(\frac{\sqrt{2}}{2}\) is not a rational number.

Option C is \(\frac{3}{\sqrt{5}}\).

• Calculate \(\sqrt{5}\): \[ \sqrt{5} \approx 2.2361 \]
• Therefore, \(\frac{3}{\sqrt{5}} \approx \frac{3}{2.2361} \approx 1.3416\).

Since \(1.3416\) cannot be expressed as a ratio of two integers, \(\frac{3}{\sqrt{5}}\) is not a rational number.

Final Answer