Question

Which of the following is a rational number?

• A. \(\sqrt{64+36}\)
• B. \(\sqrt{25+25}\)
• C. \(\sqrt{49+49}\)
• D. \(\sqrt{36+36}\)

Hint:

A square root is rational only if the radicand is a perfect square (e.g., \(100, 144\)). Otherwise, it’s irrational.

Answer 1

The Correct Option is A

Step 1: Evaluate each expression under the square root.
\(\sqrt{64+36}=\sqrt{100}=10\) (rational).
\(\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\) (irrational).
\(\sqrt{49+49}=\sqrt{98}=7\sqrt{2}\) (irrational).
\(\sqrt{36+36}=\sqrt{72}=6\sqrt{2}\) (irrational).
Step 2: Conclude.
Only option (1) simplifies to an integer, hence it is rational.