Question

How do you rationalize the denominator and simplify `(-4sqrt6 - 2sqrt18 )/( sqrt3)`?

Answer 1

`-4sqrt(2)-2sqrt(6)`

Explanation:

To Rationalize this quotient means we have to get rid of the radical from the denominator so we should multiply the numerator and denominator by `sqrt(3)`

`(-4sqrt(6)-2sqrt(18))/(sqrt(3))*(sqrt(3))/(sqrt(3))`
Knowing the property ,multiplication of two radicals that says:

`sqrt(a*b)=sqrt(a)*sqrt(b)`
`=(-4sqrt(6*3)-2sqrt(18*3))/(sqrt(3))^2`
`=(-4sqrt(2*3*3)-2sqrt(2*3*3*3))/3`
`=(-4*3sqrt(2)-2*3sqrt(6))/3`

Simplifying by `3`
`=-4sqrt(2)-2sqrt(6)`