Rationalize and simplify : `-8/sqrt(3)-10/sqrt(14)` 

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The expression `-8/sqrt 3 - 10/sqrt 14` has to be simplified.

`-8/sqrt 3 - 10/sqrt 14`

= `(-8*sqrt 3)/3 - (10*sqrt 14)/14`

= `(-8*14*sqrt 3 - 10*3*sqrt 14)/(14*3)`

= `(-112*sqrt 3 - 30*sqrt 14)/42`

= `(-56*sqrt 3 - 15*sqrt 14)/21`

The expression` -8/sqrt 3 - 10/sqrt 14 = (-56*sqrt 3 - 15*sqrt 14)/21`

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The terms `sqrt 3` and `sqrt 14` are irrational as they cannot be expressed as a fraction consisting of integers.

To simplify `-8/sqrt 3 - 10/sqrt 14` , first eliminate the irrational term from the denominator.

`-8/sqrt 3 - 10/sqrt 14`

Multiply the numerator and denominator of the first term by `sqrt 3` and the numerator and denominator of the second by `sqrt 14`

`(-8*sqrt 3)/(sqrt 3*sqrt 3) - (10*sqrt 14)/(sqrt 14*sqrt 14)`

`(-8*sqrt 3)/3 - (10*sqrt 14)/14`

Now make the denominator of both the terms equal.

`(-8*sqrt 3*14)/(3*14) - (10*sqrt 14*3)/(14*3)`

= `(-8*sqrt 3*14 - 10*sqrt 14*3)/(14*3)`

= `(-4*sqrt 3*14 - 5*sqrt 14*3)/(7*3)`

= `(-56*sqrt 3 - 15*sqrt 14)/21`

The expression `-8/sqrt 3 - 10/sqrt 14 = (-56*sqrt 3 - 15*sqrt 14)/21`

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