The value of √(5(√5(√5))).....is

Question

The value of \(\sqrt{5\sqrt{5\sqrt{5}}}......is\)

(a) 1 

(b) 2.5 

(c) 5 

(d) 25

Answer 1

(c) 5

Let x = \(\sqrt{5\sqrt{5\sqrt{5}}}......is\)

⇒ x = \(\sqrt{5x}\) ⇒ x² = 5x

⇒ x² - 5x = 0 ⇒ x (x - 5) = 0 ⇒ 0 or 5

Neglecting x = 0, we have x = 5.