A math trick that takes a little practice but is cool once you get it:
To square any two digit number in your head
1)Round the number to the nearest 10 (let's say 23 - so 20)
2)Find the "opposite" of the rounding by adding or subtracting the same amount you rounded by: 23 went down 3 to 20, so up 3 would be 26.
3)We now have two new numbers that are fairly easy to multiply in your head: 20x26. Easy way to do this:
20 x (20+6)
20x20=400;
20x6=120;
add those together, 520.
4)Now you still have that 3 that you rounded by to deal with. Square that and add it to your total: 529. 23x23 is 529.
It works with every two digit number. Some are easier to do than others (squaring anything with a 5 is super easy), but with practice you can get to do these fairly fast. There's a trick to starting to answer while you do the calculations in your head that makes it look really impressive. I used to be able to do these quickly, but I'm out of practice.
Another example, just to clarify:
74 squared. We round up and down by 4.
70x78.
70x70=4900; 70x8=560. 4900+560=5460. Add the 16 from what you rounded, you get 5476.
Hi, Shirley Temple Pudding.