The answer is not 2

Algebra Level 2

Simplify

$\sqrt{\frac{2}{\sqrt{\frac{2}{\sqrt{\frac{2}{\sqrt{\frac{2}{\cdot..}}}}}}}}$

Try this one

\sqrt{2}

\sqrt[3]{2}

\frac{\sqrt{2}}{2}

1 solution

Paul Ryan Longhas
Mar 29, 2015

Let $x = \sqrt{\frac{2}{\sqrt{\frac{2}{\sqrt{\frac{2}{\sqrt{\frac{2}{\cdot..}}}}}}}}$

$\Rightarrow x^2 = \frac{2}{\sqrt{\frac{2}{\sqrt{\frac{2}{\sqrt{\frac{2}{\cdot..}}}}}}}$

$\Rightarrow x^2 = \frac{2}{x} \Rightarrow x^3 = 2$

$\Rightarrow x = \sqrt[3]{2}$

Use \Rightarrow to signify implication.

Sharky Kesa - 6 years, 2 months ago

Thanks..... Done :D

Paul Ryan Longhas - 6 years, 2 months ago