Today's price of Shake Shack $($SHAK$)$ is $$40.$ SHAK does not pay dividends. One year from today, there are two possible states. In the $u$ state, the price of SHAK is $$80.$ In the $d$ state, the price of SHAK is $$20.$ The c$.$c$.$ risk$-$free interest rate is two percent. Assume there is no arbitrage. A root derivative has payoffs $x_u=\sqrt[\phantom{2}]{?}{S}_u$ and $x_d=\sqrt[\phantom{2}]{?}{S}_d.$ What is the price of the root derivative? Round your answer to three decimal places.