How do you simplify #asqrt27-2sqrt(3a^2)#?

1 Answer
Aug 23, 2016

Answer:

If #a in RR# then #asqrt(27)-2sqrt(3a^2)=(3a-2abs(a))sqrt(3)#

If #a>=0# then #asqrt(27)-2sqrt(3a^2)=asqrt(3)#

Explanation:

Assuming #a# is a Real number:

#asqrt(27)-2sqrt(3a^2)#

#=asqrt(3^2*3)-2sqrt(a^2*3)#

#=asqrt(3^2)sqrt(3)-2sqrt(a^2)sqrt(3)#

#=(3a-2abs(a))sqrt(3)#

If in addition #a>=0# then #3a-2abs(a) = 3a-2a=a# and

#asqrt(27)-2sqrt(3a^2) = asqrt(3)#