SOLUTION: Can you give me a formula to work out the amount of squares within a square eg. a chess board

Question 213492: Can you give me a formula to work out the amount of squares within a square eg. a chess board
Found 3 solutions by stanbon, jim_thompson5910, Theo:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
There are two dimensions: width and length
Multiply the number of squares in the width
by the number of squares in the length to
get the number of square units in the figure.
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Cheers,
Stan H.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
If you're asking just about the number of 1x1 squares, then the last post is correct. If you're asking about larger squares (2x2, 3x3, etc..), then there's more to this problem. Check out this page to see the answer.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if you are starting from the larger square, then the formula would be:
where:
x = one side of larger square.
n = number of smaller squares whose square root is an integer.
y = one side of smaller square.
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example:
one side of larger square equals 15 inches.
number of smaller squares you want to make is 64 (chessboard).
square root of 64 equals 8 which is an integer so this is a good number.
-----
formula becomes:
which becomes .
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you will be able to place 64 smaller squares into the larger square if each one side of the smaller squares is 1.875 inches.
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if your are starting from the smaller square, then the formula would be:
where:
x = one side of larger square.
n = number of smaller squares whose square root is an integer.
y = one side of smaller square.
-----
example:
you have a smaller square of 1.875 inches on a side.
you want to put together 64 of these to make a chessboard.
the formula is:
where:
x = one side of larger square.
n = number of smaller squares whose square root is an integer.
y = one side of smaller square.
-----
n = 64
y = 1.875
you plug these values into the formula to get:
which becomes
one side of the larger square is 15 inches.
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the number of smaller squares you want to fit into the larger square has to have an integer as the square root of that number. otherwise the formulas will not work.
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example:
you want to take 2 smaller squares and make a larger square out of them.
square root of 2 is not an integer so this will not work. visually you should be able to see this very easily. you simply cannot divide a larger square board into 2 and get 2 smaller square boards out of it that will fit inside the larger square board.
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