Question

10. Simplify the rational expression by rationalizing the denominator. 3 sqrt 160/sqrt 1350x A) 2 sqrt 15x/15x B) 3 sqrt 160/1350x C) 4 sqrt 15x/15x D) 4/ sqrt 45x 11.

Answer 1

The simplified expression by rationalizing the denominator is (C)
`(4 √(15x) )/(15x)`.

First we must simplify the expression:

`(3 √(160) )/(√(1350x) ) = (12 √(10) )/(15 √(6x) ) = (4 √(10) )/(5 √(6x) )`

Then we factor the rational parts and cancel it out:

`(4 √(2) √(5) )/(5 √(2) √(3x) ) = (4√(5) )/(5√(3x) )`

Then we rationalize the expression:

`(4√(5) )/(5√(3x) ) * (√(3x) )/(√(3x) ) = (4 √(15x) )/(5*3x) = (4 √(15x) )/(15x)`

Finally, the simplified expression by rationalizing the denominator is (C)
`(4 √(15x) )/(15x)`.