Question

Section: Name Rational and Irrational Numbers a) Determine if the product of
`3 √( 2)` and
`8 √(18)` is rational or irrational. Explain your answer.

Answer 1

we have

`(2√(2))(8√(18))`

Remember that

18=2(3^2)

substitute

`\begin{gathered} (2√(2))(8√(2(3^2))) \\ (2√(2))(8\cdot3√(2)) \\ (2√(2))(24√(2)) \\ (24\cdot2)(2) \\ 96 \end{gathered}`

96 is a rational number, because

96=96/1

can be written as the quotient of two integers