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

2 Answers
smendyka
Mar 10, 2018

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

Barney V.
Mar 10, 2018

(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

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