While doing some routine calculation recently, I've noticed something pretty darn strange. I have this sneaking suspicion that the result comes out of a well-known theorem, so if you can explain it to me thanks a bunch!

This is what happens:

let x = square root of 0.1:

0.31622776601683793319988935444327...

compute 1/x:

3.1622776601683793319988935444327...

See a pattern? :)

I found it pretty weird, so I picked another number at random: 5

square root of 5:

2.2360679774997896964091736687313...

1/sqrt(5):

0.44721359549995793928183473374626...

(just divide by 2, and ...)

Incidentally, this is the same as sqrt(0.2)

For certain other numbers, I don't see an easy pattern... So. What am I seeing here? TIA, all.

Ok, that was silly...

0.1 = 1/10

sqrt(0.1) = sqrt(1/10) = 1/sqrt(10)

then

1/sqrt(0.1) = sqrt(10)

So my first result really means that:

1/sqrt(10) = sqrt(10)/10

or

10 = (sqrt(10))^2

Duh... So much for that one.

Now, as to why 1/sqrt(5) = sqrt(0.2), it's even sillier.

1/sqrt(5) = sqrt(1/5) = sqrt(0.2)

Oh, I feel stupid...

Finally,

sqrt(5) = 1/sqrt(5)*10/2 = 5/sqrt(5) (well, DUH!)

Ah, the "miracles" that come out of calculators... :eek: