Which class of IP addresses is the following address in 10.10.252.123?

That would be a Class A IPv4 address.

A good way to memorize the three primary classes in classful routing is always know the ranges of the first octet for a classful IP address. An even easier way is to convert the first octet to 8-bit binary and examine the first few bits.

First Octet > [10] < .10.252.123 (in binary: [00001010])

Class A: 0-127 (the leading bit of the address is always 0)

Class B: 128-191 (the leading bits of the address are always 10)

Class C: 192-223 (the leading bits of the address are always 110)

Class D: 224-239 (the leading bits of the address are always 1110)

Class E: 240-255 (the leading bits of the address are always 1111)