No, it is not possible to construct such table using an ordinary tape measure.
Why? It is because the area of a square is s², and the square root of an area of an ordinary square (the side ) should be principal and rational, meaning it is a whole number and is positive. So if:
A = 3 m²
s² = 3 m²
s = √3 m
( The square root of 3 is not a whole number. Therefore the side is not a whole number, therefore a square table with an area of 3 m² is not possible using an ordinary tape measure.