Question

Find the value of $\sqrt{100\sqrt{100\sqrt{\mathrm{100...}}}}$ to infinity.

• A. $10$
• B. $100$
• C. ${100}^3$
• D. $\sqrt{{10}^{}}$

Answer 1

The correct option is B $100$

$\sqrt{100\sqrt{100\sqrt{100}}....\infty }$

Let $\sqrt{100\sqrt{\mathrm{100....}\infty }}=x$

square both sides

$100\sqrt{100\sqrt{\mathrm{100....}\infty }}=x^2$

$\Rightarrow 100x=x^2$

$\Rightarrow x^2-100x=0$

$\Rightarrow x=100(\because x\ne 0)$