Is the product of $3sqrt2$ and $8sqrt18$ rational or irrational?

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Answer 1 · 2017-08-01T22:06:25

See a solution process below:

We can rewrite the expression as:

$(3 * 8)(sqrt(2) * sqrt(18)) => 24(sqrt(2) * sqrt(18)) =>$

$24(sqrt(2 * 18)) => 24(sqrt(36)) => 24 * 6 => 144$

The product is rational.

Is the product of 3sqrt23sqrt2 and 8sqrt188sqrt18 rational or irrational?