Question

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

Answer 1

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

$7 \sqrt[3]{2x} - 3 \sqrt[3]{8 \times 2x} - 3 \sqrt[3]{4 \times 2x}$

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

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

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

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

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

Answer 2

Answer:

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

Step-by-step 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

$16=2^3\times2$ and $8=2^3$

$7\sqrt[3]{2x}-3\times2\sqrt[3]{2x}-3\times2\sqrt[3]{x}$

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