2023 · Q14
If the positive square root of (5 + 3√2) (5 - 3√2) is α, then what is the positive square root of 8 + 2α?
Elementary MathematicsAlgebra
- A2 + 3
- B3 - 2
- C7 - 1
- D√7 + 1
Explanation
First, α = √((5 + 3√2)(5 − 3√2)) = √(25 − 18) = √7. Then 8 + 2α = 8 + 2√7, which equals (√7 + 1)² since (√7 + 1)² = 8 + 2√7. Its positive square root is therefore √7 + 1 (D).