√2 is irrational because let's suppose √2 is a rational number. Then, we write √2=a/b where a and b are whole number, b≠0 From the equality √2=a/b, it follows that 2= a²/b²( Make all of them to the second power), or a²=2×b² Then, a is 2 times some other whole number. In symbols, a=2k where k is this other number If we substitute a=2k into the original equation 2=a²/b², this is what we get: 2=(2k)²/b² 2=4k²/b² 2b²=4k² b²=2k². This means that b² is even, from which follows again that b itself is we . And that is contradiction, and thus our original assumption (that √2 is rational). Therefore, √2 can not be rational √2=1.41421356237.. √2=1.4( rounded to the nearest tenth). Hope it help!
