`sqrt(18/13)` Simplify the expression.

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violy | High School Teacher | (Level 1) Associate Educator

Posted on

Since there is a radical expression at the bottom, we need to rationalize the denominator.
In rationalizing the denominator, we multiply the top and bottom by what we have on the denominator.
`(sqrt(18)*sqrt(13))/(sqrt(13)*sqrt(13)) = (sqrt(18)*(sqrt(13))/(sqrt(13*13)) = ((sqrt(18)*sqrt(13))/(sqrt(169)))`

Take note that` 13 * 13 = 169` , hence` sqrt(169) = 13` .

We will have:  `(sqrt(18)*sqrt(13))/13` .
We can no longer simplify the `sqrt(13)` , for the `sqrt(18)` , we will think of a perfect square number that is a factor of `18` .

Let us list the perfect square numbers:` 4, 9, 16, 25, 36, 49, 64, 81, 100, .. `

The factor of` 18 ` there is `9` , so we will use that to factor the `18` inside the radical sign.
`(sqrt(18)*(sqrt(13)))/13 = (sqrt(9)*sqrt(2)*sqrt(13))/13` .
 
We know that` 3 *3 = 9` , so `sqrt(9) = 3` .
`(sqrt(9)*sqrt(2)*sqrt(13))/13 = (3sqrt(2)*sqrt(13))/13 = (sqrt(26))/13` .

Therefore, `(sqrt(18))/(sqrt(13)) = (sqrt(26))/13` .

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Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

`sqrt(18/13)*sqrt(13/13)`

`= (sqrt(9)*sqrt(2)*sqrt(13))/13`

`(3sqrt(26))/13`

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