To determine if an expression is rational or irrational, we first simplify the expression.
2sqrt(5) * 3sqrt(8)
=2sqrt(5) * 3 sqrt(2*2^2)
=2sqrt(5) * 3sqrt(2)sqrt(2^2)
=2sqrt(5) * 3 sqrt(2) * 2
=2*3*2 * sqrt(5)*sqrt(2)
=12sqrt(2)sqrt(5)
since 2 and 5 are prime, and therefore cannot be perfect squares, their square-roots cannot be simplified further. We conclude that the given expression is irrational, because the simplified version contains square-roots of prime numbers.
Note: 1 is not considered a prime number.
