[tex]\begin{gathered} y=k\cdot\frac{x^2z^2}{\sqrt{w}\sqrt{t}} \\ \text{when, x=}2\text{,z=3,w=16,t=}3\text{ the value of y is 1} \\ 1=k\cdot\frac{(2)^2(3)^2}{\sqrt{16}\sqrt{3}} \\ 1=k\cdot\frac{(4)(9)}{(4)(\sqrt{3})} \\ 1=k\cdot\frac{9}{\sqrt{3}} \\ \text{Solving k} \\ k=\frac{\sqrt{3}}{9} \\ \text{Hence } \\ y=(\frac{\sqrt[]{3}}{9})\cdot\frac{x^2z^2}{\sqrt[]{w}\sqrt[]{t}} \\ y=\text{?, when x=}3\text{,z=}2\text{,w=}36\text{, t=1} \\ y=(\frac{\sqrt[]{3}}{9})\cdot(\frac{(3)^2(2)^2}{\sqrt{36}\sqrt{1}}) \\ y=(\frac{\sqrt[]{3}}{9})\cdot(\frac{(9)^{}(4)^{}}{(6)(1)}) \\ y=(\frac{\sqrt[]{3}}{9})\cdot(\frac{36}{6}) \\ y=(\frac{\sqrt[]{3}}{9})\cdot(6) \\ y=\frac{6\sqrt{3}}{9} \\ y=\frac{2\sqrt[]{3}}{3} \\ \text{The value of y is }\frac{2\sqrt[]{3}}{3}\approx1.1547 \end{gathered}[/tex]
