Simple question

May 2019
2
1
Michigan
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/sqrt b=x=a*sqrt b
AND c/sqrt a=y=b*sqrt 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/sqrt 42=615.670=95*sqrt 42
3990/sqrt 92=409.365=42*sqrt 95

Ex 2.
0*5=0
0/sqrt 5=0=0*sqrt 5
2.236 is not equal to 0
0/sqrt 0=undefined, cannot devide by 0
5*sqrt 0=0

Ex 3.
3*9=27
27/sqrt 9=9=3*sqrt 9
27/sqrt 3=15.588=9*sqrt 3

If anyone can tell me if this has any significance, or what it has to do with, then please contact me.

Thanks
 

skeeter

Math Team
Jul 2011
3,364
1,855
Texas
$a \cdot b =c$

note that $b=\sqrt{b} \cdot \sqrt{b}$ for $b >0$.
Substitute the radical product for $b$ in the initial equation.

$a \cdot \sqrt{b} \cdot \sqrt{b} = c$

now, divide both sides of the above equation by $\sqrt{b}$ ...
 
May 2019
2
1
Michigan
$a \cdot b =c$

note that $b=\sqrt{b} \cdot \sqrt{b}$ for $b >0$.
Substitute the radical product for $b$ in the initial equation.

$a \cdot \sqrt{b} \cdot \sqrt{b} = c$

now, divide both sides of the above equation by $\sqrt{b}$ ...
Hi Skeeter,

I understand what you're trying to do, but my question was what it had to do with, like is it some part of calculus or trig, and also, what significance does it have?

Thanks
 
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skeeter

Math Team
Jul 2011
3,364
1,855
Texas
Hi Skeeter,

I understand what you're trying to do, but my question was what it had to do with, like is it some part of calculus or trig, and also, what significance does it have?

Thanks
it's just algebra