# Simple Question

Teacher's questions

### Simple Question

Hello,

I'm no mathematician, nor am I any good at math, but I somehow came across this odd set of equations that seem to always work out, with an exception. I was just messing around on my calculator, when the following equations seemed to work themselves out to me.

IF a⋅b=c
THEN c/√b=x=a⋅√b
AND c/√a=y=b⋅√a
EXCEPT IF a or b=0

I will post some examples below, as proof.
DISCLAIMER: All numbers are rounded to the nearest thousandth.

Ex 1.
95⋅42=3990
3990/√42=615.670=95⋅√42
3990/√92=409.365=42⋅√95

Ex 2.
0⋅5=0
0/√5=0=0⋅√5
0/√0=undefined, cannot devide by 0
5⋅√=0

Ex 3.
3⋅9=27
27/√9=9=3⋅√9
27/√3=15.588=9⋅√3

If anyone can tell me if this has any significance, or what it has to do with, then please contact me. Let me clarify, as I have asked this on other forums, and people have only tried to solve the problems. I am not looking for a solution to the problems, I am simply looking for an explanation about how they lead to the corresponding answers, and what they could possibly be used for.

Thanks
Guest

### Re: Simple Question

Do you understand what "$$\sqrt{x}$$" means? The square root of x is the number whose square is equal to x: $$(\sqrt{x})^2= (\sqrt{x})(\sqrt{x})= x$$. '

So from $$c= ab$$, if we divide both sides by $$\sqrt{b}$$ we get $$\frac{c}{\sqrt{b}}= \frac{ab}{\sqrt{b}}= \frac{a(\sqrt{b})(\sqrt{b})}{\sqrt{b}}= a\sqrt{b}$$.

HallsofIvy

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