\(u=\frac{A \sqrt{x}}{x+B}\)

By the principle of homogeneity, \(x=B\) (dimensionally)

\(\Rightarrow B=[L]\)

\(\text { and }\left[ ML ^2 T ^{-2}\right]=\frac{A L^{1 / 2}}{L}\)

\({\left[ ML ^2 T ^{-2}\right]=A L^{-1 / 2}}\)

\(A=\left[ ML ^{3 / 2} T ^{-2}\right]\)