2026 · Q10
If x = 11 + 2√30, then what is the value of x^(1/2) + x^(−1/2)?
Elementary MathematicsAlgebra
- A2√2
- B2√3
- C2√5
- D2√6
Explanation
Notice that (√5 + √6)² = 5 + 6 + 2√30 = 11 + 2√30 = x, so √x = √5 + √6 (taking the positive root). Rationalising, 1/√x = 1/(√5 + √6) = √6 − √5. Hence √x + 1/√x = (√5 + √6) + (√6 − √5) = 2√6, option D.