Determine the pair of perfect squares the number falls between. For example, if finding the sqrt of 645, it falls between the sqrt of 625 which equals 25 and the sqrt of 676 which equals 26. So the sqrt of 645 has to be between 25 and 26. Where does it fall between? There are 50 numbers between 676 and 625. 645 is 20 numbers beyond 625, so 20/50 = 0.4 So the sqrt of 645 is very close to 25.4
Another method, more suitable for students in an algebra class, would be to simplify the radical using the accepted method. Then find the remaining square root with an estimation method. For example, To find SQRT(1400), simplify to SQRT(100)*SQRT(14), which is equal to 10*SQRT(14). Then find SQRT(14) by an estimation method. For square roots of perfect squares, no estimation would even be needed.
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Another method, more suitable for students in an algebra class, would be to simplify the radical using the accepted method. Then find the remaining square root with an estimation method. For example, To find SQRT(1400), simplify to SQRT(100)*SQRT(14), which is equal to 10*SQRT(14). Then find SQRT(14) by an estimation method. For square roots of perfect squares, no estimation would even be needed.
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