What is the square of root of 99999?

By seeing the options , we can infer that it is greater than $$316^2$$ . Let the value be 'a' which is above 316. Hence, lets rewrite the number :

$$\sqrt{99999}$$ = (316 + a)
99999 = $$316^2$$+ $$a^2$$ + 2(316)a
99999 = 99856 + $$a^2$$ + (632)a
Hence, we get : 143 =  $$a^2$$ + (632)a
For very small value of 'a' , $$a^2$$ can be negligible value , Hence a < $$\dfrac{\ 143}{632}$$ that will be a < 0.2262 .

Therefore 'a' should be less than 0.2262 as $$a^2$$ is present. Therefore the answer should be 316.22.