How do you simplify #(5sqrt10+9sqrt3)/(3sqrt6)#?

1 Answer
Apr 2, 2017

Answer:

#(5sqrt(15))/9+(3sqrt(2))/2#

Explanation:

Write as:

#(5sqrt(10))/(3sqrt(6))+(9sqrt(3))/(3sqrt(6))#

#=(5sqrt(10)+9sqrt(3))/(3sqrt(6))#

Getting rid of the root in the denominator

#color(green)(=(5sqrt(10)+9sqrt(3))/(3sqrt(6))color(red)(xx1)" "->" "(5sqrt(10)+9sqrt(3))/(3sqrt(6))color(red)(xx(sqrt(6))/(sqrt(6))))" #

#" "color(green)((5sqrt(10xx6)+9sqrt(3xx6))/(3(sqrt(6))^2))#

#" "color(green)((5sqrt(10xx6)+9sqrt(3xx6))/(18)#

#" "color(green)((5sqrt(2xx5xx2xx3)+9sqrt(3xx3xx2))/(18)#

#" "color(green)((10sqrt(15)+27sqrt(2))/(18)#

#" "color(green)((5sqrt(15))/9+(3sqrt(2))/2)#