Question

The value of \(\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\) (continued infinitely) is:

• A. 3
• B. 2
• C. 6
• D. 4

Answer 1

The Correct Option is A

Step 1: Let \(x = \sqrt{6+x}\). Squaring: \(x^2 = 6 + x\).
Step 2: \(x^2 - x - 6 = 0 \Rightarrow (x-3)(x+2)=0\); taking the positive root, \(x = 3\).

Quick Tip: For an infinite nested radical, set the whole expression equal to \(x\) and solve.