Question

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

Answer 1

`7 \sqrt[3]{2x} - 3 \sqrt[3]{16x} - 3 \sqrt[3]{8x}`


`7 \sqrt[3]{2x} - 3 \sqrt[3]{8 * 2x} - 3 \sqrt[3]{4 * 2x}`


`\sqrt[3]{2x} ( 7 - 3 \sqrt[3]{8} - 3 \sqrt[3]{4})`


`\sqrt[3]{2x} ( 7 - 6 - 3 \sqrt[3]{4})`


`\sqrt[3]{2x} ( 1 - 3 \sqrt[3]{4})`


`\sqrt[3]{2x} - 3 \sqrt[3]{8x}`


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

Answer 2

The simplified form of the expression is
`\sqrt[3]{2x}-6\sqrt[3]{x}`

Explanation:

Given : Expression
`7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}`

To Simplified : The expression

Solution :

Step 1 - Write the expression

`7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}`

Step 2- Simplify the roots and re-write as

`16=2^3*2` and
`8=2^3`

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

Step 3- Solve the multiplication

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

Step 4- Taking
`\sqrt[3]{2x}` common from first two terms

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

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

Therefore, The simplified form of the expression is
`\sqrt[3]{2x}-6\sqrt[3]{x}`