Squaring Numbers
between 40 and 60
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Here's a quick way to square numbers between 40 and 60.
You know the squares of 40, 50, and 60, right?
So let's show what to do for N=51 through 59.
N= ( 50+R) , where
R is between 1 and 9.
To get
N2 =
We can have first two digits (25+R) and last two digits R2.
Thus:
522=
first two digits are (25+2) and last two digits 2x2=04,
522= 2704
582=
first two digits are (25+8) and last two digits 8x8=64,
582= 3364,
For N=41 through 49.
The rule for N=41 through 49 is similar. Write N as (40+R)
for R between 1 and 9. Then N2 will have first two digits (15+R)
and last two digits (10-R)2. So:
422=
First two digits are (15+2) and last two digits (10-2)2 =64,
422=1764.
482= First two digits are (15+8) and last two digits (10-8)2 =04,
482=
2304.
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Mathematics Village