Question

simplify (sqrt3{16}). the simplified expression is (square).

Explanation:

Step1: Factor 16

We know that \(16 = 8\times2\), and \(8 = 2^3\). So we can rewrite the cube root of 16 as \(\sqrt[3]{8\times2}\).
\(\sqrt[3]{16}=\sqrt[3]{8\times2}\)

Step2: Use the property of cube roots

The property of cube roots states that \(\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}\) (where \(a = 8\) and \(b=2\) here). Since \(\sqrt[3]{8}=\sqrt[3]{2^3} = 2\), we have:
\(\sqrt[3]{8\times2}=\sqrt[3]{8}\times\sqrt[3]{2}=2\sqrt[3]{2}\)

Answer:

\(2\sqrt[3]{2}\)