Is the product of $3 \sqrt{2}$ $3sqrt2$ and $8 \sqrt{18}$ $8sqrt18$ rational or irrational?

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Is the product of $3 \sqrt{2}$ $3sqrt2$ and $8 \sqrt{18}$ $8sqrt18$ rational or irrational?

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Answer 1 · 2017-08-01T22:06:25

See a solution process below:

Explanation:

We can rewrite the expression as:

$(3 \cdot 8) (\sqrt{2} \cdot \sqrt{18}) \Rightarrow 24 (\sqrt{2} \cdot \sqrt{18}) \Rightarrow$ $(3 * 8)(sqrt(2) * sqrt(18)) => 24(sqrt(2) * sqrt(18)) =>$

$24 (\sqrt{2 \cdot 18}) \Rightarrow 24 (\sqrt{36}) \Rightarrow 24 \cdot 6 \Rightarrow 144$ $24(sqrt(2 * 18)) => 24(sqrt(36)) => 24 * 6 => 144$

The product is rational.

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Is the product of $3 \sqrt{2}$ $3sqrt2$ and $8 \sqrt{18}$ $8sqrt18$ rational or irrational?

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