Question

State whether the product of V5 and V16 is rational or irrational. Explain your answer.

Answer 1

An irrational number is a number that cannot be expressed as a fraction of any set of integers.

We have:

$\sqrt[]{5}\times\sqrt[]{16}=\sqrt[]{5}\times\sqrt[]{4^2}=\sqrt[]{5}\times4=4\sqrt[]{5}$

This is an irrational number because as earlier defined, it cannot be expressed as a fraction of any integers.