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Math Help - Help with a surds problem?

  1. #1
    ACM
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    Help with a surds problem?

    Please could someone advise me on solving this:

    If √m +√n = √(7+√48) calculate to the nearest digit m2 + n2 ?

    Thanks
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  2. #2
    ACM
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    Re: Help with a surds problem?

    Please could someone advise me on solving this:

    If m and n are rational numbers, √m +√n = √(7+√48) calculate to the nearest digit m2 + n2 ?

    Thanks
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  3. #3
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    Re: Help with a surds problem?

    Hello, ACM!

    \text{If }\sqrt{m} + \sqrt{n} \:=\:\sqrt{7+\sqrt{48}},\,\text{calculate to the nearest digit }m^2+n^2.

    Whenever I see that an expression under a square root contains a square root,
    . . I always wonder if that expression is a square.

    Inside, we have: . 7 + \sqrt{48} \:=\:7 + 4\sqrt{3} . . . . which happens to be (2 + \sqrt{3})^2

    The problem becomes: . \sqrt{m}+\sqrt{n} \;=\;\sqrt{(2 + \sqrt{3})^2}

    . . . . . . . . . . . . . . . . . . \sqrt{m}+\sqrt{n} \;=\;2 + \sqrt{3}

    Hence: . \begin{Bmatrix}m &=& 4 \\ n &=& 3\end{Bmatrix} . or vice versa.

    Therefore: . m^2 + n^2 \;=\;4^2 + 3^2 \;=\;25
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