It is often useful to know the squares of numbers without a calculator. For example, you have to paint the ceiling of a room of 12'-6"x12'-6". How much paint would you buy if a quart covers 8 square metres? You would reason as follows:
a quart covers 8 square metres = 80 sq.ft.
12.5x12.5=156.25, therefore you'll need 2 quarts of paint to cover 160 sq.ft.
In general, it is quite possible that an average person would be able to give the squares of integers up to 100 without a calculator. Some of the numbers are easily memorized, and the others can be obtained by certain 'tricks'. This article to provide some tools to memorize or calculate the square of some numbers.
| Numbers | Method |
|---|---|
| 1-25 | Memorisation |
| numbers ending in a five 15,25,35,45,... |
Remove the last digit (five), multiply the resulting number (n) by the next number (n+1), and tag on a 25 at the end of the product. Example: 45*45 4*5=20 tag on a 25 to make 2025. Calculate 45*45=2025 |
| 25-50 | Calculate the difference (d) from 50. Subtract 100*d from 2500. Add d*d to the result. Example: To calculate 47*47: d=3 Calculate 47*47=2500-300+9=2209 |
| 50-75 | Subtract 50 from the number to give d. Add 100*d to 2500. Add d*d to the result. Example: To calculate 53*53: d=3 Calculate 53*53=2500+300+9=2809 |
| 75-100 | Subtract the number (n) from 100 to give d. Calculate (n-d)*100+d*d Example: To calculate 96*96: d=4 Calculate 96*96=(92-4)*100+4*4=9200+16=9216 |
| 100-125 | Subtract 100 from the number (n) to give d. Calculate (n+d)*100+d*d Example: To calculate 108*108: d=8 Calculate 108*108=(108+8)*100+8*8=116*100+64=11664 |
Easy, isn't it? Now you'd be glad to practise you new learned skills!