I have solved this equation by two method
√3a = 50+a
Method 1
√3a-a =50
a(√3-1) = 50
a= 50/(√3-1)
a= 50/0.73 = 68.4
Method 2
a(√3-1) = 50
a = 50/(√3-1)
a =50(√3+1)/2. [by rationalizing]
a =25 * 2.73
a = 68.25
Note : I have taken √3 = 1.73 in both of the above method Still got different value of " a ".Can you please tell why this slight deviation has occured
The error occurs because you are assuming that $\sqrt{3}=1.73$. This is incorrect: it should be $\sqrt{3} \approx 1.73$. Because you are only using the approximate value of $\sqrt{3}$, it is only natural that you get an approximate answer.
It is best to work through questions like these without rounding any figures until the very end. This is because small rounding errors can accumulate. For example, if I take $\sqrt{3}$ as $1.73$, then $1000\sqrt{3}$ would be approximated as $1730$. This is more than $2$ units away from the true answer of $1732.050\ldots$. Depending on when and where you round figures, the error that results could be marginal, or it could be much greater. In your example, the true answer is $$ a=\frac{50}{\sqrt{3}-1} \approx 68.301 \, . $$ Because you rounded early, both of your answers are a little off!