Question

plzz answer no 17 in the following image through indices

Answer 1

Given that $\sqrt{a \sqrt{a \sqrt{a...} } }$ = a

It can be written as $(a(a(a...)^{1/2})^{1/2})^{1/2}$ = a

Multiplying the powers we get, $(a)^{n/2}$ = a  (Mark as equation 1)

Having same bases, therefore $\frac{n}{2} = 1$

Therefore n = 2

Putting the value of n in equation 1, $a^{2/2} = a$ ⇒ a = a

LHS = RHS, hence proved