Rationalize and simplify : `-8/sqrt(3)-10/sqrt(14)`
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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`
tonys538 | Student, Undergraduate | (Level 1) Valedictorian
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`