The square root of two is irrational. It means that you can't write it as a fraction:
Here's a proof. Assume that you could write
for some integers p and q, and that p and q have no common divisors. If you square both sides you have
So, is even, which means that also p is even, and thus there exists some number k such that
. The expression becomes
So, also is even, and thus q is also even.
But then, p and q are both even, whereas we assumed that they had no common divisors. Contraddiction.
As for the value, any calculator will give you an approximation that starts with
so, it is best approximated by 1.4.
