What number must be added to the expression 16a² - 12a to make a perfect square ?

Solution (By Examveda Team)

$$\eqalign{ & {\left( {a - b} \right)^2} = {a^2} + {b^2} + 2ab \cr & 16{a^2} - {\text{12}}a \cr & = {(4a)^2} - 2 \times 4a \times \frac{3}{2} + {\left( {\frac{3}{2}} \right)^2} \cr & {\text{Number be added}} \cr & {\text{ = }}{\left( {\frac{3}{2}} \right)^2} \cr & = \frac{9}{4} \cr} $$