How do you simplify #sqrt(3a) + 2sqrt(27a^3)#?

2 Answers
Jun 22, 2016

Answer:

#sqrt(3a)+2sqrt(27a^3)=color(green)((1+6a)(sqrt(3a))#

Explanation:

#2sqrt(27a^3)=2*sqrt(3^2*2*a^2*a)#
#color(white)("XXX")=2*sqrt((3a)^2)*sqrt(3a)#
#color(white)("XXX") =6asqrt(3a)#

So
#sqrt(3a)+2sqrt(27a^3)#
#color(white)("XXX")=sqrt(3a)+6asqrt(3a)#
#color(white)("XXX")=(1+6a)sqrt(3a)#

Jun 22, 2016

Answer:

#sqrt(3a)(6a+1)#

Explanation:

Notice that #3xx9=27->3xx3^3=27#
Also notice that #a^3=a^2xxa#

Write as:
#sqrt(3a)+2sqrt(3^2a^2xx3a)#

Take the #3^3a^a# outside the square root as #sqrt(3^2a^2)=3a#

#sqrt(3a)+(3axx2xxsqrt(3a))#

#sqrt(3a)+6asqrt(3a)#

Factor out the #sqrt(3a)#

#sqrt(3a)(1+6a)#

Or if you prefer

#sqrt(3a)(6a+1)#