Appendix J
SQUARING NUMBERS ENDING IN 5
When you multiply a number by itself (for example, 3 × 3, or 5 × 5, or 17 × 17) you are squaring it.
Seventeen squared (or 17 × 17) is written as: 17^2 . The small 2 written after the 17 tells you how many
seventeens you are multiplying. If you wrote 17^3 it would mean three seventeens multiplied together, or
17 × 17 × 17.
Now, to square any number ending in 5 you simply ignore the 5 on the end and take the number
written in front. So, if we square 75 (75 × 75) we ignore the 5 and take the number in front, which is 7.
Add 1 to the 7 to get 8. Now multiply 7 and 8 together.
7 × 8 = 56
That is the first part of the answer.
For the last part you just square 5.
5 × 5 = 25
The 25 is always the last part of the answer. The answer is 5,625.
Why does it work? Try using 70 as a reference number and you will see we are dealing with
something we already know.
Try the problem for yourself using 80 as a reference number. It works out the same.
So, for 135^2 (135 × 135) the front part of the number is 13 (in front of the 5). We add 1 to get 14. Now
multiply 13 × 14 = 182 (using the shortcut in Chapter 3).
We square 5, or just put 25 at the end of our answer.
1352 = 18,225
For that we used either 130 or 140 as a reference number.
Try squaring 965 in your head.
Ninety-six is in front of the 5.
96 + 1 = 97
96 × 97 = 9,312
Put 25 at the end for the answer.
9652 = 931,225
That is really impressive.
Test yourself
Now try these for yourself. Don’t write anything — do them all in your head.
a) 35^2
b) 85^2