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Math Help - help please its gobledegook

  1. #1
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    help please its gobledegook

    81 to the 3/4 I know the answer is 27 but how

    and

    express square root of 2 over square root of 2 + 1 in the form a+bsquare root2, where a and b are integers
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  2. #2
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    Quote Originally Posted by mathsfool View Post
    81 to the 3/4 I know the answer is 27 but how

    and

    express square root of 2 over square root of 2 + 1 in the form a+bsquare root2, where a and b are integers
    81^{\frac34} = \left(3^4\right)^{\frac34} =\left( \left(3^4\right)^{\frac14}\right)^3 = 3^3 = 27
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  3. #3
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    Quote Originally Posted by mathsfool View Post
    ...

    express square root of 2 over square root of 2 + 1 in the form a+bsquare root2, where a and b are integers
    I hope you mean:

    \frac{\sqrt{2}}{\sqrt{2} + 1}

    If so:

    \frac{\sqrt{2}}{\sqrt{2} + 1}\cdot \frac{\sqrt{2} - 1}{\sqrt{2} - 1} = \frac{2-\sqrt{2}}{2-1} = 2-1\cdot \sqrt{2}
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