Question

write the difference in its simplest form.
\sqrt3{24} - 7\sqrt3{10}
\sqrt3{24} - 7\sqrt3{10} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify \(\sqrt[3]{24}\)

Factor 24 to find the perfect cube factor. \(24 = 8\times3\), and \(\sqrt[3]{8}=2\). So, \(\sqrt[3]{24}=\sqrt[3]{8\times3}=\sqrt[3]{8}\times\sqrt[3]{3}=2\sqrt[3]{3}\).

Step2: Substitute back into the expression

The original expression is \(\sqrt[3]{24}-7\sqrt[3]{10}\). Substituting the simplified form of \(\sqrt[3]{24}\), we get \(2\sqrt[3]{3}-7\sqrt[3]{10}\). Since \(\sqrt[3]{3}\) and \(\sqrt[3]{10}\) are not like radicals (they have different radicands), we cannot combine them further.

Answer:

\(2\sqrt[3]{3} - 7\sqrt[3]{10}\)