Evaluate \sqrt{11 \sqrt{11 \sqrt{11 \sqrt{11....... \infty}}}}

Foundation

Mathematics Foundation

Basics of Quadratic Equation

Maximum and Minimum of Quadratic

Location of Roots of Quadratic

Question

Evaluate

\sqrt{11 \sqrt{11 \sqrt{11 \sqrt{11....... \infty}}}}

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Let,

y = \sqrt{11 \sqrt{11 \sqrt{11 \sqrt{11....... \infty}}}}

\Rightarrow y = \sqrt{11. y}

\Rightarrow y^{2} = 11 y

\Rightarrow y (y - 11) = 0

\Rightarrow y = 0, 11

But

y

cann't be

0

∴ y = 11