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

Respuesta :

we have

[tex](2\sqrt{2)}(8\sqrt{18})[/tex]

Remember that

18=2(3^2)

substitute

[tex]\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}[/tex]

96 is a rational number, because

96=96/1

can be written as the quotient of two integers