Question

The value of \( (6 + \sqrt{125}) - (3 + \sqrt{5}) + (1 - 4\sqrt{5}) \) is:

• A. A rational number
• B. An irrational number
• C. Not real
• D. None of these

Hint:

Irrational terms cancel each other if they are identical in opposite signs.

Answer 1

The Correct Option is A

Expanding: \[ (6 + 5\sqrt{5}) - (3 + \sqrt{5}) + (1 - 4\sqrt{5}). \] \[ (6 - 3 + 1) + (5\sqrt{5} - \sqrt{5} - 4\sqrt{5}). \] \[ 4 + 0 = 4. \] Since the result is a rational number, the answer is correct.