Question

What is the following sum?

Answer 1

Answer: Choice B

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

In word form, this is 12 b squared (RootIndex 3 StartRoot 2 a EndRoot

Or you could say 12b^2 times the cube root of 2a

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Work Shown:

$3b^2\sqrt[3]{54a}+3\sqrt[3]{2ab^6}\\\\3b^2\sqrt[3]{27*2a}+3\sqrt[3]{b^6*2a}\\\\3b^2\sqrt[3]{(3)^3*2a}+3\sqrt[3]{(b^2)^3*2a}\\\\3b^2\sqrt[3]{(3)^3}*\sqrt[3]{2a}+3\sqrt[3]{(b^2)^3}*\sqrt[3]{2a}\\\\3b^2*3*\sqrt[3]{2a}+3*b^2*\sqrt[3]{2a}\\\\9b^2\sqrt[3]{2a}+3b^2\sqrt[3]{2a}\\\\(9b^2+3b^2)\sqrt[3]{2a}\\\\\boldsymbol{12b^2\sqrt[3]{2a}}$

The idea here is that we break the cube roots into smaller pieces, so we pull out perfect cubes when factoring.