Question

How do you rationalize the denominator and simplify `sqrt15/(sqrt15-sqrt13)`?

Answer 1

See a solution process below:

Explanation:

To rationalize the denominator multiply the fraction by the appropriate form of `1`

`(color(red)(sqrt(15)) + color(red)(sqrt(13)))/(color(red)(sqrt(15)) + color(red)(sqrt(13))) xx sqrt(15)/(sqrt(15) - sqrt(13)) =>`

`(color(red)(sqrt(15))sqrt(15) + color(red)(sqrt(13))sqrt(15))/(color(red)(sqrt(15))sqrt(15) - color(red)(sqrt(15))sqrt(13) + color(red)(sqrt(13))sqrt(15) - color(red)(sqrt(13))sqrt(13)) =>`

`(15 + sqrt(color(red)(13) * 15))/(15 - 0 - 13) =>`

`(15 + sqrt(195))/2`

Answer 2

`(15+sqrt195)/2`

Explanation:

`sqrt15/(sqrt15-sqrt13)`

`:.color(magenta)((sqrt15+sqrt13)/(sqrt15+sqrt13)=1`

`:.sqrt15/(sqrt15-sqrt13)xxcolor(magenta)((sqrt15+sqrt13)/(sqrt15+sqrt13)`

`:.color(magenta)(=sqrt15xxsqrt15=15`

`:.=(sqrt15(sqrt15+sqrt13))/((sqrt15-sqrt13)(sqrt15+sqrt13))`

`:.=(sqrt15(sqrt15+sqrt13))/(15-13)`

`:.=(sqrt15(sqrt15+sqrt13))/2`

`:.=(15+sqrt13sqrt15)/2`

`:.=(15+sqrt 195)/2`