what is the following sum?\n$3b^{2}(\\sqrt3{54a}) + 3(\\sqrt3{2ab^{6}})$\n$6b^{2}(\\sqrt3{2a})$\n$12b^{2}(\\s…

what is the following sum?\n$3b^{2}(\\sqrt3{54a}) + 3(\\sqrt3{2ab^{6}})$\n$6b^{2}(\\sqrt3{2a})$\n$12b^{2}(\\sqrt3{2a})$\n$6b^{2}(\\sqrt6{2a})$\n$12b^{2}(\\sqrt6{2a})$

what is the following sum?\n$3b^{2}(\\sqrt3{54a}) + 3(\\sqrt3{2ab^{6}})$\n$6b^{2}(\\sqrt3{2a})$\n$12b^{2}(\\sqrt3{2a})$\n$6b^{2}(\\sqrt6{2a})$\n$12b^{2}(\\sqrt6{2a})$

Answer

Explanation:

Step1: Simplify $\sqrt[3]{54a}$

We know that $54a = 27\times2a$, so $\sqrt[3]{54a}=\sqrt[3]{27\times2a}= 3\sqrt[3]{2a}$. Then $3b^{2}\sqrt[3]{54a}=3b^{2}\times3\sqrt[3]{2a}=9b^{2}\sqrt[3]{2a}$.

Step2: Simplify $\sqrt[3]{2ab^{6}}$

Since $\sqrt[3]{2ab^{6}}=b^{2}\sqrt[3]{2a}$, then $3\sqrt[3]{2ab^{6}} = 3b^{2}\sqrt[3]{2a}$.

Step3: Find the sum

$3b^{2}\sqrt[3]{54a}+3\sqrt[3]{2ab^{6}}=9b^{2}\sqrt[3]{2a}+3b^{2}\sqrt[3]{2a}=(9 + 3)b^{2}\sqrt[3]{2a}=12b^{2}\sqrt[3]{2a}$.

Answer:

$12b^{2}\left(\sqrt[3]{2a}\right)$