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

1 Answer
Mia
Jun 17, 2016

#-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)#

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