Proof That The Square Root Of 2 Is Not Equal To A Decimal Fraction
is not equal to a decimal fraction.
In other words...
square root of 2 is not equal to p/q
If we square both sides, we get 2=p squared over q squared.
If we multiply both side by q squared, we get 2q squared = p squared
Okay, here are our possibilities for p and q
p is odd and q is odd
p is even and q is even
p is odd and q is even
p is even and q is odd
For the statement, 2q squared = p squared to be true, it MUST be true
for all the above situations.
Therefore, if we can prove it's not true for just ONE of the situations,
then we have proven that the square root of two is not equal to a
decimal fraction.
Let's take this one.
p is odd and q is even
an odd number squared is always odd. So p squared for p being odd results
in an odd number.
Now let's go to q being even.
An even number squared is always even.
Any number multiplied by 2 is always even.
Therefore, 2q squared is an even number.
p squared = odd
q squared = even
odd does NOT equal even.
Therefore, the square root of 2 is NOT equal to a decimal fraction.
I hope you found this educational and entertaining.
Yes, math CAN be fun.
Read A Post.
Subscribe to a Newsletter
KimWinfrey.Com
Sal
When the Roads and Paths end, learn to guide yourself through the wilderness
Beyond the Path
You might not like what I say - but I believe it.
Build it, make money, then build some more
Some old school smarts would help - and here's to Rob Toth for his help. Bloody good stuff, even the freebies!