Answer
$a)$ $\sqrt[3]{x^{4}}+\sqrt[3]{8x}=(x+2)\sqrt[3]{x}$
$b)$ $4\sqrt{18rt^{3}}+5\sqrt{32r^{3}t^{5}}=4(5rt^{2}+3t)\sqrt{2rt}$
Work Step by Step
$a)$ $\sqrt[3]{x^{4}}+\sqrt[3]{8x}$
Simplify each individual term:
$\sqrt[3]{x^{4}}+\sqrt[3]{8x}=x\sqrt[3]{x}+2\sqrt[3]{x}=...$
Evaluate the sum by adding only the coefficients:
$...=(x+2)\sqrt[3]{x}$
$b)$ $4\sqrt{18rt^{3}}+5\sqrt{32r^{3}t^{5}}$
Simplify each individual term:
$4\sqrt{18rt^{3}}+5\sqrt{32r^{3}t^{5}}=4(3)t\sqrt{2rt}+5(4)rt^{2}\sqrt{2rt}=...$
$...=12t\sqrt{2rt}+20rt^{2}\sqrt{2rt}$
Evaluate the sum by adding only the coefficients:
$...=(20rt^{2}+12t)\sqrt{2rt}$
Take out common factor $4$ from the expression inside the parentheses:
$...=4(5rt^{2}+3t)\sqrt{2rt}$
