# The Value of √ 6 + √ 6 + √ 6 + . . . . is - Mathematics

MCQ

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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Q 7 | Page 83