Question

station 1 simplifying radicals ma.912. simplify the following radical: (sqrt3{128}) (\bigcirc) 10 (\bigcirc) (5sqrt3{2}) (\bigcirc) (3sqrt3{2}) (\bigcirc) (4sqrt3{2}) (\bigcirc) (10sqrt3{2}) (\bigcirc) (6sqrt3{2})

Explanation:

Step 1: Factorize 128

We know that \(128 = 64\times2\), and \(64 = 4^{3}\) (since \(4\times4\times4 = 64\)). So we can rewrite \(128\) as \(4^{3}\times2\).
\(\sqrt[3]{128}=\sqrt[3]{4^{3}\times2}\)

Step 2: Use the property of radicals

The property of radicals states that \(\sqrt[n]{ab}=\sqrt[n]{a}\times\sqrt[n]{b}\) (for \(a\geq0,b\geq0\) and \(n\) is a positive integer). Also, \(\sqrt[n]{a^{n}} = a\) when \(n\) is odd.
Applying these properties:
\(\sqrt[3]{4^{3}\times2}=\sqrt[3]{4^{3}}\times\sqrt[3]{2}\)
Since \(\sqrt[3]{4^{3}} = 4\) (because the cube root and the cube cancel out for real numbers), we get:
\(4\times\sqrt[3]{2}=4\sqrt[3]{2}\)

Answer:

\(4\sqrt[3]{2}\) (corresponding to the option \(4\sqrt[3]{2}\))