Help with a math problem

[Jarvan]

Ok.. I now feel stupid. But these darn SQRT's are throwing me for a loop when trying to figure out this problem.

If any of our math wiz's would be willing to help, I would appreciate it.

g=200b/(SQRT((c*d)*SQRTe)*(200*SQRTf))

I need to solve for e.

I am not sure if it's the lack of sleep, the screaming kids, or the damn SQRT's that are making my brain mush, but I just can't seem to get it.

[TheEschaton]

I like to think of square roots as something to the one-half power, it makes it easier to do math with.


g = 200b/(SQRT((c*d) * SQRT e) * (200 * SQRT f) )

g = 200b/ ((c*d) * e^1/2)^1/2 * 200 * f^1/2

1/g = [((c*d) * e^1/2)^1/2 * 200 * f^1/2]/200b

200b/g = (c * d * e^1/2)^1/2 * 200 * f^1/2

200b/[g * (200 * f^1/2)] = (c * d * e^1/2)^1/2

40000b^2/[g * (200 * f^1/2)]^2 = c * d * e^1/2

40000b^2/{[g * (200 * f^1/2)]^2 * (c * d)} = e^1/2

1600000000b^4/{[g * (200 * f^1/2)]^2 * (c * d)}^2 = e
1600000000b^4/{[g * (200 * f^1/2)]*[g * (200 * f^1/2)] * (c * d)}^2
1600000000b^4/{g^2 * 40000 * f * (c * d)}^2
1600000000b^4/(g^4 * 1600000000 * f^2 * c^2 * d^2)
b^4/(g^4 * f^2 * c^2 * d^2) = e


As far as I can tell. But it's late. Should be able to be further simplified, I'm sure.

If e = 81, c = d = 2, b = 5, and f = 49, you'd get

g = 1000/8400, or 10/84, or 5/42. If you plug that into the last equation with e absent, you have

e = 1,000,000,000,000/{[5/42 * 1400]^2 * 4}^2
e = 1,000,000,000,000/{[7000/42]^2 * 4}^2
e = 1,000,000,000,000/{49,000,000/1764 * 4}^2
e = 1,000,000,000,000/{196,000,000/1764}^2
e = 1,000,000,000,000/{38,416,000,000,000,000/3,111,696}
e = 1,000,000,000,000/{1,000,000,000,000/81}
e = 81