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# The Value of √ 6 + √ 6 + √ 6 + . . . . is - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Completing the Square

#### Question

The value of $\sqrt{6 + \sqrt{6 + \sqrt{6 +}}} . . . .$ is

• 4

• 3

• -2

• 3.5

#### Solution

Let x = sqrt(6 +sqrt(6+sqrt(6+sqrt(6+).....

Squaring both sides we get

x = sqrt(6 +sqrt(6+sqrt(6+sqrt(6+).....

x^2 = 6 + x

x^2 - x - 6 = 0

x^2 = 3x + 2x - 6 = 0

x (x - 3) + 2(x - 3) = 0

(x - 3)(x + 2) = 0

(x - 3) = 0

x = 3

or

(x +2) = 0

x = -2

The value of x cannot be negative.

Thus, the value of x = 3

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Solution The Value of √ 6 + √ 6 + √ 6 + . . . . is Concept: Solutions of Quadratic Equations by Completing the Square.
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