Squaring 2-digit numbers (other than the numbers that end in 5)
Let's say you want to square 58. Square each digit and write a partial answer. 5x5 = 25. 8x8 = 64. Write down 2564 to start. Then, multiply the two digits of the number you're squaring together, 5x8=40.
Double this product: 40x2=80, then add a 0 to it, getting 800.
Add 800 to 2564 to get 3364.
This is pretty complicated so let's do more examples.
32x32. The first part of the answer comes from squaring 3 and 2.
3x3=9. 2x2 = 4. Write down 0904. Notice the extra zeros. It's important that every square in the partial product have two digits.
Multiply the digits, 2 and 3, together and double the whole thing. 2x3x2 = 12.
Add a zero to get 120. Add 120 to the partial product, 0904, and we get 1024.
56x56. The partial product comes from 5x5 and 6x6. Write down 2536.
5x6x2 = 60. Add a zero to get 600.
56x56 = 2536+600 = 3136.
One more example: 67x67. Write down 3649 as the partial product.
6x7x2 = 42x2 = 84. Add a zero to get 840.
67x67=3649+840 = 4489.