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    what is the square root of 216

    0  Views: 1299 Answers: 2 Posted: 10 years ago

    2 Answers

    square root(216) = 14.6969385


    Here's one way to figure it out yourself:


    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.

    chelleanne

    I rather use the calculator for square roots that is not a whole number. The guessing method is too much for me.

    Without a calculator:


    14^2 = 196


    15^2 = 225


    square root of 216 lies between 14 and 15


    14.9^2 = 222.01  >  too high


    14.5^2 = 210.25  >  too low


    GUESS


    14.8^2 = 219.04    >     too high


    14.7^2 = 216.09    >     too high


    14.6^2 = 213.16    >     too low


    14.69^2 = 215.7961  >  too low


    14.695^2 = 215.943025  >  too low


    14.699^2 = 216.060601  >  too high


    14.698^2 = 216.031204  >  too high


    14.697^2 = 216.001809  >  too high


    14.696^2 = 215.972416  >  too low


    14.6965^2 = 215.98711225  >  too low


    14.6966^2 = 215.99005156  >  too low


    14.6969^2 = 215.99886961  >  too low


    14.69695^2 = 216.0003393025  >   high


    14.69694^2 = 216.0000453636  >   high


    14.69693^2 = 215.9997514249  >  close


    14.696939^2 = 216.000015969721  >   high


    14.696938^2 = 215.999986575844   >   close


    I'm going to stop now.


    The square root of 216 at six decimals is:


    Answer: 14.696938


    I rather use the calculator!

    Bob/PKB

    Me, too. It's good for us to know HOW to figure it out w/o the calculator, though, like you did. What a hassle!!


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