Well and , that leaves you to try 7,8 and 9.
Algebraically?
I suppose you could say that
So 7 squared lies between 40 and 50, and adapt this for the other numbers.
Hello, ManuLi!
Is there any easy way to find squares of numbers between 40 and 50, 60 and 90?
There is a trick for squaring numbers "near 50",
Let .where is the "deviation from 50".
Then: .
So, in the hundreds-place is: .
. . . followed by , the deviation-squared.
Example: .
The deviation is: .
The answer is: .
. .followed by: .
Therefore: .
Example: .
The deviation is: .
The answer is: .
. .followed by: .
Therefore: .
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Consecutive squares differ by consecutive odd numbers.
. .
If we know one square, we can crank out the next few squares.
For example: .
Double the 60 and add 1: .
That is the odd number we will add.
. .