Question

why root 23 is irrational​

Answer 1

Assume it was rational then √23

√23 = a/b, 

where a, b are integers, 

and 

therefore 23 = a²/b². 

So a² = 23b². 

Now √a² = a = an integer, 

and 

therefore √23b² = integer. 

√23b²= b*√23

√23 is not an integer,  so the assumption was wrong. 

Therefore √23 is not rational.

Answer 2

Root 23 is irrational because the value of 4.795.................. which is non terminating hence it is irrational number.