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