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Question
The simplest rationalising factor of \[\sqrt[3]{500}\] is
Options
\[\sqrt[3]{2}\]
\[\sqrt[3]{5}\]
\[\sqrt{3}\]
none of these
Solution
Given that: `3sqrt500` To find simplest rationalizing factor of the given expression we will factorize it as
`3sqrt500 = 3sqrt(125xx 4)`
`= 3sqrt(5xx5xx5xx 4)`
`= 3sqrt((5))^3 xx 3sqrt4`
` = 5 3sqrt4`
The rationalizing factor of `5 3sqrt4`is, `3sqrt2`since when we multiply given expression with this factor we get rid of irrational term.
Therefore, rationalizing factor of the given expression is `3sqrt2`
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