Question

What is the simplified form of the following expression? 7(^3 square root 2x) - 3 (^3 square root 16x) -3 (^3 square root 8x)

Answer 1

The third option listed:
`\sqrt[3]{2x} -6\sqrt[3]{x}\\`

Explanation:

We start by writing all the numerical factors inside the qubic roots in factor form (and if possible with exponent 3 so as to easily identify what can be extracted from the root):

`7\sqrt[3]{2x}  -3\sqrt[3]{16x} -3\sqrt[3]{8x} =\\=7\sqrt[3]{2x}  -3\sqrt[3]{2^32x} -3\sqrt[3]{2^3x} =\\=7\sqrt[3]{2x}  -3*2\sqrt[3]{2x} -3*2\sqrt[3]{x}=\\=7\sqrt[3]{2x}  -6\sqrt[3]{2x} -6\sqrt[3]{x}`

And now we combine all like terms (notice that the only two terms we can combine are the first two, which contain the exact same radical form:

`7\sqrt[3]{2x}  -6\sqrt[3]{2x} -6\sqrt[3]{x}=\\=\sqrt[3]{2x} -6\sqrt[3]{x}`

Therefore this is the simplified radical expression:
`\sqrt[3]{2x} -6\sqrt[3]{x}\\`