If $${\text{ }}2*3 = \sqrt {13} $$   and 3 * 4 = 5, then the value of 5 * 12 is ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Clearly, }}a*b = \sqrt {{a^2} + {b^2}} \cr & \therefore 5*12 \cr & = \sqrt {{5^2} + {{12}^2}} \cr & = \sqrt {25 + 144} \cr & = \sqrt {169} \cr & = 13 \cr} $$