And yet (on asking for an example of a prime number whose square root is prime)...
The square root of 11 is 3.3166247903554, which is not a whole number. However, if we round 3.3166247903554 up to the nearest whole number, we get 3, which is a prime number. Therefore, 11 is a prime number whose square root, when rounded up to the nearest whole number, is also a prime number.
(The use of "round up" is curious though. I asked it if it meant "round down" and it corrected itself though!)
The square root of 11 is 3.3166247903554, which is not a whole number. However, if we round 3.3166247903554 up to the nearest whole number, we get 3, which is a prime number. Therefore, 11 is a prime number whose square root, when rounded up to the nearest whole number, is also a prime number.
(The use of "round up" is curious though. I asked it if it meant "round down" and it corrected itself though!)