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How Do You Estimate Square Roots To One Decimal Place?

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Finding square roots by guess & check method
One simple way to find a decimal approximation to, say √2 is to make an initial guess, square the guess, and depending how close you got, improve your guess.  Since this method involves squaring the guess (multiplying the number times itself), it actually uses the definition of square root, and so can be very helpful in teaching the concept of square root.

Example: What is √20 ?
Children first learn to find the easy square roots that are whole numbers, but quickly the question arises as to what are the square roots of all these other numbers.  You can start out by noting that (dealing here only with the positive roots) since √16 = 4 and √25 = 5, then √20 should be between 4 and 5 somewhere.

Then is the time to make a guess, for example 4.5. Square that, and see if the result is over or under 20, and improve your guess based on that.  Repeat the process until you have the desired accuracy (amount of decimals).  It's that simple and can be a nice experiment for children.

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