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Math Help - Approximate of square root of 2

  1. #1
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    Approximate of square root of 2

    62/45 < square root of 2 < 64/45

    Use these bounds to write the value of square root of 2 to an appropriate degree of accuracy?
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  2. #2
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    Quote Originally Posted by Natasha1 View Post
    62/45 < square root of 2 < 64/45

    Use these bounds to write the value of square root of 2 to an appropriate degree of accuracy?
    Perhaps 63/45 and long division ....
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  3. #3
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    I'm not sure about the depth of this question. For starters, a reasonable approximation of sqrt(2) given those two inequalities would be the average of the bounds. In other words, try calculating the average of 62/45 and 64/45, and see how well this value serves as an approximation of the square root of 2.
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  4. #4
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    I'm asking this because I don't understand how to go about answering a question like this one. Never done it before...

    Would it be wise to then write something like this

    62/45 = 1.377777777....
    64/45 = 1.422222222....
    and 63/45 = 1.4

    so square root of 2 is approximately 1.4
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  5. #5
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    \displaystyle\frac{63}{45}=\frac{(9)7}{(9)5}=\frac  {7}{5}=1\frac{2}{5}=1.4

    which is maybe the idea, so yes it's a "reasonable" approximation.
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