Question

Find the value of $\sqrt{a\sqrt{a\sqrt{a.....\infty }}}$

• A. $a$
• B. $a^2$
• C. $a^3$
• D. $\sqrt{a}$

Answer 1

The correct option is A $a$

Let $x=\sqrt{a\sqrt{a\sqrt{a.....\infty }}}$

$\Rightarrow x^2=a\sqrt{a\sqrt{a-\infty }}=ax$

$\Rightarrow x=0,a$ As $x\ne 0\Rightarrow x=a$