Question 74430
{{{sqrt(12x^2y^3)(sqrt( 8xy))}}}Both square roots can be broken up since {{{sqrt(xy)=sqrt(x)*sqrt(y)}}}
{{{(sqrt(12)*sqrt(x^2)*sqrt(y^3))(sqrt(8)*sqrt(x)*sqrt(y))}}}
{{{(sqrt(4*3)*(x^2)^(1/2)*(y^3)^(1/2))(sqrt(4*2)*(x)^(1/2)*(y)^(1/2))}}}Rewrite the radicals as exponents
{{{(sqrt(4)*sqrt(3)*(x^2)^(1/2)*(y^3)^(1/2))(sqrt(4)*sqrt(2)*(x)^(1/2)*(y)^(1/2))}}}Break up the square roots
{{{(2*sqrt(3)*(x^2)^(1/2)*(y^3)^(1/2))(2*sqrt(2)*(x)^(1/2)*(y)^(1/2))}}}
{{{(2*sqrt(3)*x*y^(3/2))(2*sqrt(2)*(x)^(1/2)*(y)^(1/2))}}}When multiplying bases with exponents you add the exponents.
{{{(4*sqrt(3)*sqrt(2)*x^(1+1/2)*y^(3/2+1/2))}}}
{{{(4*sqrt(3)*sqrt(2)*x^(3/2)*y^(2))}}}So there's the simplified answer.