multiply radical 5x^2y by radical 25xy^6?

multiplying same root can be combined
sqrt 5x^2y * sqrt 25xy^6 = sqrt (5x^2y * 25xy^6)
sqrt 5x^2y * sqrt 25xy^6 = sqrt ( 5*25 * x^2*x * y*y^6)
sqrt 5x^2y * sqrt 25xy^6 = sqrt (125x^3y^7)
sqrt 5x^2y * sqrt 25xy^6 = 5xy^3 sqrt( 5xy)

√(5x^2y) * √(25xy^6)
= √[5 * x^2 * y] * √[5^2 * x * (y^3)^2]
= x√(5y) * 5y^3√x
= 5xy^3√(5xy)

sqrt(125x^3y^7)
=5xy^3 sqrt(5xy)

5x^2y by radical 25xy^6
x rad 5y times 5y^3 rad x
5xy^3 rad 5xy