Exams › SSC CGL (Prelims) › General

Evaluate \(\sqrt{30 + \sqrt{30 + \sqrt{30 + \cdots}}}\).

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

Correct answer: 6

Solution

Let the expression be \(x\). Then \(x=\sqrt{30+x}\), so \(x^2=30+x\). This gives \(x^2-x-30=0\), or \((x-6)(x+5)=0\). Since the value is positive, \(x=6\).

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