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SSC CHSL 12 Nov 2025 Shift 2 Paper

Question : 64 of 100

Marks: +1, -0

\sqrt{12+\sqrt{12+\sqrt{12+…}}}

Solution:

Concept:

When a nested radical repeats infinitely, we can set the entire expression equal to a variable and substitute the inner part with the same variable.

Explanation:

Let

x = \sqrt{12 + \sqrt{12 + \sqrt{12 + ...}}}

The pattern inside repeats, so

x = \sqrt{12 + x}

Square both sides:

x^2 = 12 + x

Rearrange:

x^2 - x - 12 = 0

Factor:

(x - 4)(x + 3) = 0

Thus,

x = 4

x = -3

Since a square root cannot be negative, discard

x = -3

Answer:

The value is 4. Option B.

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