# Simplify expression

• April 19th 2013, 01:34 AM
mrtn
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)

• April 19th 2013, 02:01 AM
Draco93
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.
• April 19th 2013, 02:18 AM
mrtn
Re: Simplify expression
Sorry. Would this be all right:

Attachment 28024
• April 19th 2013, 04:43 AM
Soroban
Re: Simplify expression
Hello, mrtn!

Quote:

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

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:

. . $\displaystyle\frac{\sqrt{Adh}}{\sqrt{2}} + \frac{\sqrt{Adh}}{\sqrt{2}} \;=\; \frac{2\sqrt{Adh}}{\sqrt{2}} \;=\;\sqrt{2}\sqrt{Adh} \;=\;\sqrt{2Adh}$
• April 19th 2013, 04:57 AM
cindrella
Re: Simplify expression
i like algibra
• April 19th 2013, 05:29 AM
mrtn
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 Attachment 28027

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.
• April 19th 2013, 03:26 PM
unkle
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