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Math Help - Simplify expression

  1. #1
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    Simplify expression

    Hi there

    Can anyone tell me how to simplify this expression

    d/sqrt(2*A*d/h)*A+sqrt(2*A*d/h)/2*h

    to this expression

    sqrt(2*A*d*h)

    Thank you i advance
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  2. #2
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    Re: Simplify expression

    Would be more easier to read if we had some brackets to make the expression less ambiguous. Otherwise, there's a bit of guess work involved.
    Thanks from MarkFL and mrtn
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  3. #3
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    Re: Simplify expression

    Sorry. Would this be all right:

    Simplify expression-unavngivet.png
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  4. #4
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    Re: Simplify expression

    Hello, mrtn!

    \text{Show that: }\:\left(\frac{d}{\sqrt{\frac{2Ad}{h}}}\times A\right) + \left(\frac{\sqrt{\frac{2Ad}{h}}}{2} \times h\right) \;=\;\sqrt{2Adh}

    The first product is:

    . . \displaystyle\dfrac{d}{\frac{\sqrt{2}\sqrt{A}\sqrt  {d}}{\sqrt{h}}} \cdot A  \;=\; \frac{Ad\sqrt{h}}{\sqrt{2}\sqrt{A}\sqrt{d}} \;=\; \frac{\sqrt{A}\sqrt{d}\sqrt{h}}{\sqrt{2}} \;=\;\frac{\sqrt{Adh}}{\sqrt{2}}


    The second product is:

    . . \displaystyle\dfrac{\frac{\sqrt{2}\sqrt{A}\sqrt{d}  }{\sqrt{h}}}{2} \cdot h \;=\; \dfrac{\sqrt{2}\sqrt{A}\sqrt{d}\,h}{2\sqrt{h}}\;= \; \frac{\sqrt{A}\sqrt{d}\sqrt{h}}{\sqrt{2}} \;=\; \frac{\sqrt{Adh}}{\sqrt{2}}


    Their sum is:

    . . \displaystyle\frac{\sqrt{Adh}}{\sqrt{2}} + \frac{\sqrt{Adh}}{\sqrt{2}} \;=\; \frac{2\sqrt{Adh}}{\sqrt{2}} \;=\;\sqrt{2}\sqrt{Adh} \;=\;\sqrt{2Adh}
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  5. #5
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    Re: Simplify expression

    i like algibra
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  6. #6
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    Re: Simplify expression

    Thank you Soroban.

    My next challenge is to simplify the first product as you just wrote (I know I am on deep water):

    Show that Simplify expression-unavngivet1.png

    I need to know step by step, which math rules are used etc. to get the final expressions.

    Do you know any software, which are able to help me with this?

    Or else I can keep you guys busy, like forever.
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  7. #7
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    Re: Simplify expression

    algebra.help gets you half way there I am student and I am sure there is a law to follow for algebra hope the link helps you to help yourself
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