Question 167645
{{{sqrt(3x^6)* sqrt(27x^13)=sqrt((3x^6)(27x^13))=sqrt((3*27)(x^6*x^13))=sqrt(81x^(19))=sqrt(81)*sqrt(x^19)=9x^9*sqrt(x)}}}



--------------------


Answer:



So {{{sqrt(3x^6)* sqrt(27x^13)=9x^9*sqrt(x)}}}




------------------



Here are some side notes



1) All variables are positive so this means that {{{x>=0}}}



2) To multiply variables with exponents (the same variables) simply add the exponents {{{x^6*x^13=x^(6+13)=x^19}}}



3) The goal to simplify this is to break 19 into 18+1 where 18 is a multiple of 2 (that way, we can take the square root)

 {{{sqrt(x^19)=sqrt(x^(18+1))=sqrt(x^18*x^1)=sqrt((x^9)^2*x)=sqrt((x^9)^2)*sqrt(x)=x^9*sqrt(x)}}}