<Dd> 20 n 2 + 20 n + 4 = 4 m 2 + 4 m (\ displaystyle 20n ^ (2) + 20n + 4 = 4m ^ (2) + 4m) </Dd> <Dd> which reduces to: <Dl> <Dd> 5 n 2 + 5 n + 1 = m 2 + m (\ displaystyle 5n ^ (2) + 5n + 1 = m ^ (2) + m) </Dd> </Dl> </Dd> <Dl> <Dd> 5 n 2 + 5 n + 1 = m 2 + m (\ displaystyle 5n ^ (2) + 5n + 1 = m ^ (2) + m) </Dd> </Dl> <Dd> 5 n 2 + 5 n + 1 = m 2 + m (\ displaystyle 5n ^ (2) + 5n + 1 = m ^ (2) + m) </Dd>

Proof that root 5 is an irrational number