Question

The value of $\sqrt{2\sqrt{2}\sqrt{2\cdots \cdots \cdots \infty }}$ is 2.

• A. True
• B. False

Answer 1

The correct option is B

False

Let , $\sqrt{2\sqrt{2}\sqrt{2\cdots \cdots \cdots \infty }}=x$

$\Rightarrow \sqrt{2\sqrt{2}\sqrt{2\cdots \cdots \cdots \infty }}=x^2$ (Squaring on both sides)

$\Rightarrow 2\sqrt{2}=x^2$

$\Rightarrow x^2-2\sqrt{2}x=0$

$\Rightarrow x(x-2\sqrt{2})=0$

So, x=0 or $x=2\sqrt{2}$.