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The value of √(12 + √(12 + √(12 +...))) is

1. 3.464
2. 3.932
3. 4.000
4. 4.444

Correct answer: 4.000

Solution

The expression can be set equal to x, leading to the equation x = √(12 + x). Squaring both sides gives x² = 12 + x, which simplifies to x² - x - 12 = 0. Solving this quadratic equation yields x = 4 as the positive solution, confirming that the value is 4.000.

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