2023 · Q25
If x = √(4√(4√(4√4…))) then what is the value of x?
Elementary MathematicsAlgebra
- A2
- B4
- C8
- D16
Explanation
Denote the infinite nested radical by x; then it satisfies x = √(4x). Squaring gives x² = 4x, and since x > 0, x = 4 (B).
If x = √(4√(4√(4√4…))) then what is the value of x?
Explanation
Denote the infinite nested radical by x; then it satisfies x = √(4x). Squaring gives x² = 4x, and since x > 0, x = 4 (B).