Question:
The value of \( (6 + \sqrt{125}) - (3 + \sqrt{5}) + (1 - 4\sqrt{5}) \) is:
The value of \( (6 + \sqrt{125}) - (3 + \sqrt{5}) + (1 - 4\sqrt{5}) \) is:
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Irrational terms cancel each other if they are identical in opposite signs.
Updated On: Oct 27, 2025
- A rational number
- An irrational number
- Not real
- None of these
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The Correct Option is A
Solution and Explanation
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.
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