2(∛3) - ∛18 is the quotient of the given expression [6 - 3(∛6)] / ∛9.
"Surds are irrational numbers which are represented in square root form and further cannot be simplified in simple form."
According to the question,
[tex]\frac{6-3(\sqrt[3]{6)} }{\sqrt[3]{9} }[/tex]
Multiply and divide the given expression by surd ∛3 we get,
[tex]\frac{6-3(\sqrt[3]{6)} }{\sqrt[3]{9} }[/tex]×[tex]\frac{\sqrt[3]{3} }{\sqrt[3]{3} }[/tex]
= [tex]\frac{6\sqrt[3]{3} -3(\sqrt[3]{18)} }{\sqrt[3]{27} }[/tex]
=[tex]\frac{3(2\sqrt[3]{3} -(\sqrt[3]{18)}) }{3 }[/tex]
=[tex]2(\sqrt[3]{3} )-\sqrt[3]{18}[/tex]
Hence, 2(∛3) - ∛18 is the quotient of the given expression
[6 - 3(∛6)] / ∛9.
Learn more about surds here
https://brainly.com/question/91095
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