Square Root Problem: Equal Expressions?

[storoi1990]

1. Homework Statement [/b]

i have this thing:

2u$$\sqrt{}um$$

is this expression the same as:

2u^3/2*m^1/2

Homework Equations

The Attempt at a Solution

 

[snshusat161]

it means $$2u^{3/2}m^{1/2}$$ Where is m in your expression.

 

[storoi1990]

great! i am just bad with latex :)

 

[storoi1990]

so later on i get this

$$\lambda$$ = $$3u^{1/2}m^{1/2}$$

and $$\lambda$$ = $$u^{3/2}/m^{1/2}$$

i am supposed to solve this as an equation:

$$3u^{1/2}m^{1/2}$$ = $$u^{3/2}/m^{1/2}$$

but how?

 

[snshusat161]

$$3u^{1/2}.m^{1/2}$$ = $$\frac{u^{3/2}}{m^{1/2}}$$

that is equal to u = 3m

 

[storoi1990]

how did you do that? did you cross multiply or something?

 

[snshusat161]

yes, I've done cross multiplication. I'm giving you some more detail.

take $$m^{1/2}$$ from denominator on right hand side to numerator at left hand side and similarly take $$3u^{1/2}$$ from numerator at right hand side to denominator at right hand side. Now you have to know that whenever me multiply powers add up and whenever we divide power subtract up. Do you have any doubt now.

 

[storoi1990]

i am stil having some issues with this.

so is it correct that i would end up with:

$$m^{1/2}*3u^{1/2}m^{1/2}$$ = $$u^{3/2}/m^{1/2}*3u^{1/2}$$

 

[snshusat161]

no, you have moved $$m^{1/2}$$ from right side to left hand side and its correct but now you have to delete it from the right hand side, and similar with the other one.

 

[snshusat161]

in computer language you don't have to copy and paste actually you have to cut and paste.

 

[storoi1990]

okey so then i end up with:

$$m^{1/2}m^{1/2}$$ = $$u^{3/2}3u^{1/2}$$

and so:

$$m$$ = $$3u^{4/2}$$

am i right?

 

[snshusat161]

no, some other members may help you. I'm tiered using latex. If you still confused, write your all the problem, if you can scan then scan and post it to www.monbattle.com . I'll solve each and every problem for you in a detailed manner, scan it and post it there so that you can copy and understand.

last thing I should add for your problem is that when you cross multiply, take digits from top of one side to bottom of other side and bottom on one side to top of other side.

 

[storoi1990]

okey, thank you very much for your help :)