Question

Section: Name Rational and Irrational Numbers a) Determine if the product of $3 \sqrt{ 2}$ and $8 \sqrt{18}$ is rational or irrational. Explain your answer.

Answer 1

we have

$(2\sqrt{2)}(8\sqrt{18})$

Remember that

18=2(3^2)

substitute

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

96 is a rational number, because

96=96/1

can be written as the quotient of two integers