Originally Posted by
masters Hi wolfhound,
Now, now let's be nice.
Here's the flow from where you started:
$\displaystyle 4t^2-8s^2=0$
$\displaystyle -8s^2=-4t^2$
$\displaystyle s^2=\frac{1}{2}t^2$
$\displaystyle s=\sqrt{\frac{1}{2}t^2}$
$\displaystyle s=\frac{\sqrt{t^2}}{\sqrt{2}}$
$\displaystyle s=\frac{t}{\sqrt{2}}$
This is what Pickslides gave you. Now, you must rationalize the denominator.
$\displaystyle s=\frac{t}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}$
$\displaystyle s=\frac{t\sqrt{2}}{2}$
$\displaystyle {\color{green}s=\frac{1}{2}t\sqrt{2}}$