The question says "Simplify. Express in simplest radical form." 3 square root of 3/13  

Expert Answers
sciencesolve eNotes educator| Certified Educator

Supposing that you need to reduce `3sqrt(3/13)` to the simplest form, you need to use the following property of square roots, such that:

`sqrt(a/b) = (sqrt a)/(sqrt b)`

`sqrt(3/13) = (sqrt 3)/(sqrt 13)`

Since you need to reduce the given number to the simplest form, hence, the denominator should not be irrational. You need to rationalize the denominator performing thge multiplication of both, numerator and denominator, by `sqrt 13` , such that:

`3(sqrt 3)/(sqrt 13) = 3((sqrt 3)(sqrt 13))/((sqrt 13)(sqrt 13))`

`3(sqrt 3)/(sqrt 13) = 3((sqrt (3*13)))/13 => 3(sqrt 3)/(sqrt 13) = 3((sqrt (39)))/13`

Hence, reducing the number to the simplest form using the rationalization of denominator, yields `3(sqrt 3)/(sqrt 13) = 3((sqrt (39)))/13.`

mariloucortez eNotes educator| Certified Educator

To simplify  `3 sqrt(3/13)`   apply the property:  `sqrt(a/b) = sqrt(a)/sqrt(b)`

So you have `3 sqrt(3)/sqrt(13).`

Simplifying radical numbers or expression means that there should be no radical in the denominator part. You do this by rationalizing. It means that you multiply the numerator and denominator by `sqrt(13)`

` 3 sqrt(3)/sqrt(13) * sqrt(13)/sqrt(13)`

 `= 3 (sqrt(3) * sqrt(13))/(sqrt(13)*sqrt(13))`

`= 3 sqrt(3*13)/sqrt(13*13)`

`= 3 sqrt(39)/13`

` `  Therefore the simplified form of `3 sqrt(3/13) = 3 sqrt(39)/13.`


pramodpandey | Student
3 squart(3/13)=(3/13)squart(39) Here you need to rationalize denominator.