If x = 3 + 2√2, find √x.
Aptitude
Surds and Indices
Difficulty: Easy
Choose an option
-
A√2 + 1
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B√2 − 1
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C2√2
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D3
Answer
Correct Answer: √2 + 1
Explanation
Concept / Approach
- Try to express x as a perfect square of the form (√2 ± 1)^2.
Step-by-step calculation(√2 + 1)^2 = (√2)^2 + 2·√2·1 + 1^2 = 2 + 2√2 + 1 = 3 + 2√2Therefore, x = (√2 + 1)^2 ⇒ √x = √2 + 1
Verification / Alternative(√2 − 1)^2 = 2 − 2√2 + 1 = 3 − 2√2 ≠ x, so the positive root is √2 + 1.
Final Answer√2 + 1