What is the sum and classification of 3/10 and square root of 10

3/10 is a rational number, but sqrt (10) is not (it's irrational).

Thus, the sum of these two quantities is also irrational.

3/10 + sqrt (10) cannot be simplified further.

However, you could express both in decimal fraction notation and obtain the approx. sum:

0.3 + 3.162 = 3.462 (approx)