what is the following sum?\n$sqrt3{125x^{10}y^{13}}+sqrt3{27x^{10}y^{13}}$\n$8x^{3}y^{4}(sqrt3{xy})$\n$15x^{6…

what is the following sum?\n$sqrt3{125x^{10}y^{13}}+sqrt3{27x^{10}y^{13}}$\n$8x^{3}y^{4}(sqrt3{xy})$\n$15x^{6}y^{8}(sqrt3{xy})$\n$15x^{3}y^{4}(sqrt3{xy})$\n$8x^{6}y^{8}(sqrt3{xy})$

what is the following sum?\n$sqrt3{125x^{10}y^{13}}+sqrt3{27x^{10}y^{13}}$\n$8x^{3}y^{4}(sqrt3{xy})$\n$15x^{6}y^{8}(sqrt3{xy})$\n$15x^{3}y^{4}(sqrt3{xy})$\n$8x^{6}y^{8}(sqrt3{xy})$

Answer

Answer:

A. $8x^{3}y^{4}(\sqrt[3]{xy})$

Explanation:

Step1: Simplify first cube - root term

We know that $125x^{10}y^{13}=5^{3}\cdot x^{9}\cdot x\cdot y^{12}\cdot y$. So, $\sqrt[3]{125x^{10}y^{13}}=\sqrt[3]{5^{3}\cdot x^{9}\cdot x\cdot y^{12}\cdot y}=5x^{3}y^{4}\sqrt[3]{xy}$.

Step2: Simplify second cube - root term

We know that $27x^{10}y^{13}=3^{3}\cdot x^{9}\cdot x\cdot y^{12}\cdot y$. So, $\sqrt[3]{27x^{10}y^{13}}=\sqrt[3]{3^{3}\cdot x^{9}\cdot x\cdot y^{12}\cdot y}=3x^{3}y^{4}\sqrt[3]{xy}$.

Step3: Find the sum

$\sqrt[3]{125x^{10}y^{13}}+\sqrt[3]{27x^{10}y^{13}}=(5x^{3}y^{4}+3x^{3}y^{4})\sqrt[3]{xy}=8x^{3}y^{4}\sqrt[3]{xy}$.