ABCDEFGHIJKLMNOPQRSTUVWXYZ
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See a geometric demonstration at GeoGebraTube:
http://ggbtu.be/m3129269
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The square root of a number N is the length of the side of a square whose area is N.
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This method starts with a square whose side is a too-big guess.
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Find the area of this square. If it's N, you're done. If not:
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Calculate how much excess area you need to get rid of.
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Divide by 2 to get the area of one of two strips to cut off the top and right of the square.
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But when you cut off the strips, they're not equal:
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a small square in the upper right was subtracted twice, but only removed once.
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So the area is still too big, by the area of this square.
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Repeat until the side of the remaining square is as close as you need.
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Try it! Change ONLY the numbers in shaded cells, B16 and A19:
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N = 5
(Number to find the square root of)
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StepGuess: side of squareArea of squareExcess area1/2 of excess area
width of strips to cut off
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139420.6666666667
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22.3333333335.4444444440.44444444440.22222222220.09523809524
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32.2380952385.0090702950.0090702947850.0045351473920.002026342452
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42.2360688965.0000041060.0000041060637310.0000020530318650.0000009181433852
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52.2360679775000
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62.2360679775000
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72.2360679775000
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82.2360679775000
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92.2360679775000
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102.2360679775000
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112.2360679775000
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122.2360679775000
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