the first step to solving this is to factor out the first perfect square [tex] \sqrt{12^{2} x^{7} y^{5} } [/tex] now factor out the second perfect square [tex] \sqrt{ 12^{2} x^{6} X x y^{5} } [/tex] then factor out the second perfect square [tex] \sqrt{ 12^{2} x^{6} X x y^{4} X y} [/tex] the root of a product is equal to the product of the roots of each factor [tex] \sqrt{ 12^{2} } [/tex] [tex] \sqrt{ x^{6} } [/tex] [tex] \sqrt{ y^{4} } [/tex] [tex] \sqrt{xy} [/tex] reduce the index of the radical and exponent with 2 of the first square root 12[tex] \sqrt{ x^{6} } [/tex] [tex] \sqrt{ y^{4} } [/tex] [tex] \sqrt{xy} [/tex] reduce the index of the radical and exponent with 2 of the second square root 12x³[tex] \sqrt{ y^{4} } [/tex] [tex] \sqrt{xy} [/tex] reduce the index of the radical and exponent with 2 of the third square root 12x³y²[tex] \sqrt{xy} [/tex] this means that the correct answer to your question is 12x³y²[tex] \sqrt{xy} [/tex] . let me know if you have any further questions :)