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

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Answer 1 · 2017-04-02T19:27:51

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

Write as:

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

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

Getting rid of the root in the denominator

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

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

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

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

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

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

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