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