Which of the following is a rational number?

Question

Which of the following is a rational number?

1. A. √2
2. B. √3
3. C. √4 (Correct answer)
4. D. √5

Correct Answer

Option C — √4

Detailed Solution & Explanation

The correct answer is √4.

Key Points

• √4 = 2, which can be written as the fraction 2/1, so it is a rational number.
• √2, √3 and √5 are square roots of numbers that are not perfect squares, and are therefore irrational — their decimal expansions never terminate or repeat.

Additional Information

• A rational number is any number expressible as p/q with q ≠ 0; this includes all integers, terminating decimals and recurring decimals.
• The rule to apply quickly: √n is rational only when n is a perfect square — 1, 4, 9, 16, 25, 36 and so on.
• The irrationality of √2 was among the earliest results in Greek mathematics and is still a standard proof by contradiction.