Question

Find the product with its conjugate pair of $\sqrt{x{y}^2}-\sqrt{x^{2}y}$

• A. conjugate pair $=\sqrt{x^2}+\sqrt{x^{2}y}$, product $x{y}^2-x^{2}y$
• B. conjugate pair $=\sqrt{x{y}^2}+\sqrt{x^{2}y}$, product $x{y}^2-x^{2}y$
• C. conjugate pair $=\sqrt{x{y}^2}+\sqrt{x^{2}y}$, product $x{y}^2-xy$
• D. conjugate pair $=\sqrt{x{y}^2}+\sqrt{x^2}$, product $x{y}^2-x^{2}y$

Answer 1

The correct option is B conjugate pair $=\sqrt{x{y}^2}+\sqrt{x^{2}y}$, product $x{y}^2-x^{2}y$

Conjugate of $\sqrt{x{y}^2}-\sqrt{x^{2}y}$ is $\sqrt{x{y}^2}+\sqrt{x^{2}y}$
and
$(\sqrt{x{y}^2}-\sqrt{x^{2}y})(\sqrt{x{y}^2}+\sqrt{x^{2}y})$
$=\left(\right(\sqrt{x{y}^2}{)}^2-\left(\sqrt{x^{2}y}{)}^2\right)=x{y}^2-x^{2}y$