1. ## 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)

2. ## 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.

3. ## Re: Simplify expression

Sorry. Would this be all right:

4. ## Re: Simplify expression

Hello, mrtn!

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

The first product is:

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

The second product is:

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

Their sum is:

. . $\displaystyle \displaystyle\frac{\sqrt{Adh}}{\sqrt{2}} + \frac{\sqrt{Adh}}{\sqrt{2}} \;=\; \frac{2\sqrt{Adh}}{\sqrt{2}} \;=\;\sqrt{2}\sqrt{Adh} \;=\;\sqrt{2Adh}$

5. ## Re: Simplify expression

i like algibra

6. ## 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

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.

7. ## 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