Square root of 1 plus nested square roots of 1 plus n equals 2; n = 64.
This equation relates the square root of a number (n) to a constant value (2) through an iterative process. Let's solve it step-by-step:
1: Define variables.
Let:
a = √n
b = √(1 + a)
2: Substitute the definition of b into the equation.
√(1 + b) = 2
3: Square both sides of the equation.
1 + b = 4
4: Subtract 1 from both sides.
b = 3
5: Substitute the definition of b back to find a.
√(1 + √n) = 3
6: Square both sides again.
1 + √n = 9
7: Subtract 1 from both sides.
√n = 8
Therefore, the solution for n is:
n = √8^2
n = 64