



1 < 7 < 8 => 1,9^{3} = 6.859 < 7 1,91^{3} = 6.967871 < 7 < 1,92^{3} = 7.077888 => 1,91 < < 1,92 1,911^{3} = 6.978821031 < 7, 1,912^{3} = 6.989782528 < 7, 1,913^{3} = 7.000755497 > 7 => 1,912 < < 1,913 => 1,912 < < 1,913 
prove: (a) is irrational (b) is irrational, if p is a prime number 
(a) assume: is rational
=> 
(b) assume: is rational 
Setting x = y it follows, if x^{2} = x * x can be divided
by p then x can be divided by p.