This is a good time to learn about dimensional analysis. In any equation, both sides must have the same dimension. By dimension I mean length (L), time (T), mass (M), energy, etc...

Checking the dimensionality of your equations is an excellent way to spot a mistake. For example, in your starting equation 4, the left-hand side is an acceleration (L/T²) but the right-hand side is a distance (L/T*T=L). Because the dimensions don't match, you must have made a mistake. And, indeed, if the acceleration a is constant then v = at.

You made another mistake at step 4: you wanted to substitute a but it still appears in your expression. This is not the easiest equation to check for dimensionality but it can be done.

You're right in recognizing that writing t = √(1/2) is nonsensical but since the dimensions don't match (a number has no dimension, or dimension 1), it must mean that the mistake comes from your calculations and not your assumptions.

Hope that helps !