Exams › SSC CGL (Prelims) › General

Evaluate the infinite nested radical sqrt(30 + sqrt(30 + sqrt(30 + ...))).

1. 5
2. 3
3. 10
4. 6

Correct answer: 6

Solution

Let x = sqrt(30 + x), so x^2 - x - 30 = 0, which factors as (x-6)(x+5)=0. The positive root is x = 6.

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