Question

A. 2y^2 sqrt3xB. 12y^2 sqrtxC. 2y sqrt3xy D. 2y^2 sqrt6x

Answer 1

Given the expression:

$\text{ }\sqrt[]{4xy^3}\text{ }\cdot\text{ }\sqrt[]{6y}$

Let's simplify the expression:

$\text{ }\sqrt[]{4xy^3}\text{ }\cdot\text{ }\sqrt[]{6y}$$\text{ (}4)^{\frac{1}{2}}(x)^{\frac{1}{2}}(y^3)^{\frac{1}{2}}\text{ x (}6)^{\frac{1}{2}}(y)^{\frac{1}{2}}$

Let's arrange the expression with similar ones beside them:

$\text{ (}4)^{\frac{1}{2}}\text{(}6)^{\frac{1}{2}}(y^3)^{\frac{1}{2}}(y)^{\frac{1}{2}}(x)^{\frac{1}{2}}$$(\sqrt[]{4\text{ x 6}})(\sqrt[]{y^3\text{ x }y})(\sqrt[]{x})$$\text{ (}\sqrt[]{24})(\sqrt[]{y^4})(\sqrt[]{x})$$\text{ (2}\sqrt[]{6})(y^2)(\sqrt[]{x})$$\text{ (2)(y}^2)\sqrt[]{(6)(x)}$$\text{ 2y}^2\sqrt[]{6x}$

Therefore, the answer is 2y²√6x.