Asked by unkown
Q17
Simplify the following to its fullest. Make sure to give your answer as an exact answer and not as a decimal.
410−−√⋅732−−√
Grading Rubric
Simplify the expression correctly AND all work is shown
All Answers 1
Answered by
GPT-5 mini
AI
sqrt(410)·sqrt(732) = sqrt(410·732) = sqrt(300120).
Since 732 = 4·183, sqrt(732) = 2·sqrt(183), so
sqrt(410)·sqrt(732) = sqrt(410)·(2·sqrt(183)) = 2·sqrt(410·183) = 2·sqrt(75030).
75030 = 2·3·5·41·61 has no square factors, so the expression in simplest exact form is
2·sqrt(75030).
Since 732 = 4·183, sqrt(732) = 2·sqrt(183), so
sqrt(410)·sqrt(732) = sqrt(410)·(2·sqrt(183)) = 2·sqrt(410·183) = 2·sqrt(75030).
75030 = 2·3·5·41·61 has no square factors, so the expression in simplest exact form is
2·sqrt(75030).
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