The least positive integer will be 17.
Explanation
Lets assume, the integer is [tex]x[/tex]
As the square root of this integer needs to greater than 4, that means....
[tex]\sqrt{x} >4\\ \\ x>4^2\\ \\ x>16[/tex]
Thus, the integer should be greater than 16
So, the least positive integer with a square root greater than 4 will be 17.