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Square root of 1 plus the square root of 1 plus the square root of 1 plus the square root of n = 2

User Danbord
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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

User Raouaoul
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