- #1
johann1301
- 217
- 1
Homework Statement
In this task we will show that √2 is irrational. Assume that √2 = a/b where both a and b are natural numbers. Let a = p1p2p3...pn, and b = q1q2q3...qm be the prime factors
a) explain why 2q1q1q2q2q3q3...qmqm = p1p1p2p2p3p3...pnpn
√2=a/b
b√2=a
√2q1q2q3...qm=p1p2p3...pn
(√2(q1q2q3...qm))2=(p1p2p3...pn)2
2q1q1q2q2q3q3...qmqm = p1p1p2p2p3p3...pnpn
b) explain why there can't be the same amount of 2-factors on the left and the right
Im stuck on this one...
Is it because then a and b could be further shortened/divided?