Our math prof (who moonlighted as a "mathemagician") taught us a trick for two-digit squares:
For e.g. 23 x 23, subtract three from the first number, add three to the second, and then add 3² to the product. So 20 x 26 + 9, the idea being that multiplying by a multiple of 10 is easier to do mentally.
For e.g. 23 x 23, subtract three from the first number, add three to the second, and then add 3² to the product. So 20 x 26 + 9, the idea being that multiplying by a multiple of 10 is easier to do mentally.