Question

What is the following sum

Answer 1

Answer:

2nd option is the correct answer

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

Step-by-step explanation:

$3 {b}^{2} \bigg( \sqrt[3]{54a} \bigg) + 3 \bigg( \sqrt[3]{2a {b}^{6} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{27 \times 2a} \bigg) + 3 \bigg( \sqrt[3]{2a {( {b}^{2} )}^{3} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{ {3}^{3} \times 2a} \bigg) + 3 \bigg({\sqrt[3]{{( {b}^{2} )}^{3}2a} } \bigg) \\ \\ = 3 {b}^{2} \times 3 \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 9 {b}^{2} \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)$

Answer 2

Answer:

second option:  12b²(∛2a)

Step-by-step explanation:

you can break $\sqrt[3]{54a}$ into $\sqrt[3]{3^3(2a)}$ which equals 3$\sqrt[3]{2a}$

you can break $\sqrt[3]{2ab^6}$ into $\sqrt[3]{2ab^3b^3}$ which equals b²$\sqrt[3]{2a}$

now we can simplify: (3b² ·  3$\sqrt[3]{2a}$) + 3b²$\sqrt[3]{2a}$ = 9b²$\sqrt[3]{2a}$ + 3b²$\sqrt[3]{2a}$

this equals 12b²$\sqrt[3]{2a}$