How do you multiply and simplify \frac { 5\sqrt { 3} * 3\sqrt { 15} } { 4\sqrt { 5} * 2\sqrt { 75} }?

1 Answer
May 5, 2017

(5sqrt(3)*3sqrt(15))/(4sqrt(5)*2sqrt(75))=(9sqrt(5))/(8sqrt(15)

Explanation:

(5sqrt(3)*3sqrt(15))/(4sqrt(5)*2sqrt(75))

=(5*3sqrt(15**3))/(4*2sqrt(75**5)

=(5*3sqrt(5*3*3))/(4*2sqrt(5*5*3*5)

=(15*sqrt(5*3^2))/(8*sqrt(5*5*3*5)

=(15*3*sqrt(5))/(8*sqrt(5*3*5^2)

=(15*3*sqrt(5))/(8*5*sqrt(5*3)

=(45*sqrt(5))/(40*sqrt(15)

=(9*sqrt(5))/(8*sqrt(15)