Find the value of the given expression

$$\sqrt{5\sqrt{5\sqrt{5\sqrt{\dots \infty}}}}$$​

Correct option is D

Given:

$$\sqrt{5\sqrt{5\sqrt{5\sqrt{\dots \infty}}}}$$

​Concept Used:

If $$x = \sqrt{a\sqrt{a\sqrt{a\cdots}}}$$​, then

$$x = \sqrt{a \cdot x}$$

$$x^2 = a \cdot x$$

​​ Solution:

Let $$x = \sqrt{5x}$$​​

​$$x^2 = 5x$$​​

​$$x^2 - 5x = 0$$​​

​$$x(x - 5) = 0$$​​
 x = 0 or x = 5

Since the expression is positive, we do not consider 0.

Thus, the correct answer is (d).