what is the following sum?\n5x(\\sqrt3{x^{2}y}) + 2(\\sqrt3{x^{5}y})\n\\(7x(\\sqrt6{x^{2}y})\\)\n\\(7x^{2}(\\…

what is the following sum?\n5x(\\sqrt3{x^{2}y}) + 2(\\sqrt3{x^{5}y})\n\\(7x(\\sqrt6{x^{2}y})\\)\n\\(7x^{2}(\\sqrt6{xy^{2}})\\)\n\\(7x^{2}(\\sqrt3{xy^{2}})\\)\n\\(7x(\\sqrt3{x^{2}y})\\)

what is the following sum?\n5x(\\sqrt3{x^{2}y}) + 2(\\sqrt3{x^{5}y})\n\\(7x(\\sqrt6{x^{2}y})\\)\n\\(7x^{2}(\\sqrt6{xy^{2}})\\)\n\\(7x^{2}(\\sqrt3{xy^{2}})\\)\n\\(7x(\\sqrt3{x^{2}y})\\)

Answer

Explanation:

Step1: Simplify the second - radical term

We know that $\sqrt[3]{x^{5}y}=\sqrt[3]{x^{3}\cdot x^{2}y}=x\sqrt[3]{x^{2}y}$. So, $2\sqrt[3]{x^{5}y}=2x\sqrt[3]{x^{2}y}$.

Step2: Combine like - terms

The first term is $5x\sqrt[3]{x^{2}y}$ and the second term is $2x\sqrt[3]{x^{2}y}$. Then $5x\sqrt[3]{x^{2}y}+2x\sqrt[3]{x^{2}y}=(5x + 2x)\sqrt[3]{x^{2}y}$.

Step3: Calculate the coefficient

$5x+2x = 7x$. So the sum is $7x\sqrt[3]{x^{2}y}$.

Answer:

$7x\left(\sqrt[3]{x^{2}y}\right)$