The correct option is D 3 Let √( 6+√( 6+√( 6+√( 6 ) + ) #160;) #160;) ....∞ = x Squaring on both the sides,we get x ^ 2 =6+√( 6+√( 6+√( 6+√( ...

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Cube-Root of Fractional Numbers

Evaluate √6...

Question

Evaluate $\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 +}}}} . . . . . \infty$

2.45

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2.59

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2.79

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3

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Solution

The correct option is D $3$
Let $\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} +}}} . . . . \infty = x$
Squaring on both the sides,we get
$x^{2} = 6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} +}}} . . . . \infty$
$x^{2} - x = 6, x^{2} - 3 x + 2 x - 6 = 0$
$(x - 3) (x + 2) = 0$
$x$ cannot be negative as it is under the under root,
$∴ \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} +}}} . . . . \infty = 3$

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