This question is essentially just determining whether you understand the definition of integers and square roots. The square root of a quantity is a number that when multiplied with itself gives that quantity. The square root of 68 is expressed as:
√68 = 8.25
The square root of 68 is roughly 8.25. Now, an integer is simply a whole number, which is a number that is not a fraction. Therefore, the smallest integer that is greater than 8.25 is simply the next whole number, which is 9.
The smallest integer greater than the square root of 68 is 9.