Question

The simplest rationalising factor of  \[\sqrt[3]{500}\] is 

Options

• \[\sqrt[3]{2}\]

• \[\sqrt[3]{5}\]

• \[\sqrt{3}\]

• none of these

Answer 1

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`