Question

1. write the expression in simplest form. write your answer as a radical expression.

\\( \sqrt3{\frac{7}{4}} = \square \\)

Explanation:

Step1: Use the property of cube roots

We know that \(\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}\) for \(a = 7\) and \(b = 4\). So, \(\sqrt[3]{\frac{7}{4}}=\frac{\sqrt[3]{7}}{\sqrt[3]{4}}\).

Step2: Rationalize the denominator

Multiply the numerator and denominator by \(\sqrt[3]{4^{2}}\) (since \(\sqrt[3]{4}\times\sqrt[3]{4^{2}}=\sqrt[3]{4^{3}} = 4\)).

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Answer:

\(\frac{\sqrt[3]{112}}{4}\)