The value of \(\sqrt{5\sqrt{5\sqrt{5}}}......is\)(a) 1 (b) 2.5 (c)

1.	The value of \(\sqrt{5\sqrt{5\sqrt{5}}}......is\)(a) 1 (b) 2.5 (c) 5 (d) 25
Answer» (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.

The value of \(\sqrt{5\sqrt{5\sqrt{5}}}......is\)(a) 1 (b) 2.5 (c) 5 (d) 25

Answer»

(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.