Question 214122
{{{sqrt(45)*sqrt(250)}}} Start with the given expression.



{{{sqrt(9*5)*sqrt(25*10)}}} Factor each radicand into a product in which one factor is a perfect square (the largest perfect square factor)



{{{sqrt(9)*sqrt(5)*sqrt(25)*sqrt(10)}}} Break up the roots.



{{{3*sqrt(5)*5*sqrt(10)}}} Take the square root of the perfect squares 9 and 25 to get 3 and 5.



{{{3*5*sqrt(5*10)}}}Recombine the roots.



{{{15*sqrt(50)}}} Multiply



{{{15*sqrt(25*2)}}} Factor 50 into 25*2 (take note how 25 is the largest perfect square that goes into 50)



{{{15*sqrt(25)*sqrt(2)}}} Break up the root.



{{{15*5*sqrt(2)}}} Take the square root of 25 to get 5.



{{{75*sqrt(2)}}} Multiply



So {{{sqrt(45)*sqrt(250)=75*sqrt(2)}}}