Find x: if √(x + √(x + √(x… ∞))) = 6

Solution:

The factor of a number which when multiplied by itself gives the same number. For example, both 2 and -2 are the square roots of 4.

Let us proceed step by step

From the given data

√(x + √(x + √(x + … ∞))) = 6 ....... (1)

Squaring on both sides, we get (x + √(x + √(x + … ∞)) = 36

Let √(x + √(x + … ∞)) = 6

x + 6= 36

x = 36 - 6

x = 30

Hence, the value of x is 30.

Find x: if √(x + √(x + √(x… ∞))) = 6

Summary:

The value of x for the given expression is 6.