Respuesta :
[tex]7 \sqrt[3]{2x} - 3 \sqrt[3]{16x} - 3 \sqrt[3]{8x}[/tex]
[tex]7 \sqrt[3]{2x} - 3 \sqrt[3]{8 \times 2x} - 3 \sqrt[3]{4 \times 2x}[/tex]
[tex] \sqrt[3]{2x} ( 7 - 3 \sqrt[3]{8} - 3 \sqrt[3]{4})[/tex]
[tex] \sqrt[3]{2x} ( 7 - 6 - 3 \sqrt[3]{4})[/tex]
[tex] \sqrt[3]{2x} ( 1 - 3 \sqrt[3]{4})[/tex]
[tex] \sqrt[3]{2x} - 3 \sqrt[3]{8x}[/tex]
[tex] \sqrt[3]{2x} - 6 \sqrt[3]{x}[/tex]
[tex]7 \sqrt[3]{2x} - 3 \sqrt[3]{8 \times 2x} - 3 \sqrt[3]{4 \times 2x}[/tex]
[tex] \sqrt[3]{2x} ( 7 - 3 \sqrt[3]{8} - 3 \sqrt[3]{4})[/tex]
[tex] \sqrt[3]{2x} ( 7 - 6 - 3 \sqrt[3]{4})[/tex]
[tex] \sqrt[3]{2x} ( 1 - 3 \sqrt[3]{4})[/tex]
[tex] \sqrt[3]{2x} - 3 \sqrt[3]{8x}[/tex]
[tex] \sqrt[3]{2x} - 6 \sqrt[3]{x}[/tex]
Answer:
The simplified form of the expression is [tex]\sqrt[3]{2x}-6\sqrt[3]{x}[/tex]
Step-by-step explanation:
Given : Expression [tex]7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}[/tex]
To Simplified : The expression
Solution :
Step 1 - Write the expression
[tex]7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}[/tex]
Step 2- Simplify the roots and re-write as
[tex]16=2^3\times2[/tex] and [tex]8=2^3[/tex]
[tex]7\sqrt[3]{2x}-3\times2\sqrt[3]{2x}-3\times2\sqrt[3]{x}[/tex]
Step 3- Solve the multiplication
[tex]7\sqrt[3]{2x}-6\sqrt[3]{2x}-6\sqrt[3]{x}[/tex]
Step 4- Taking [tex]\sqrt[3]{2x}[/tex] common from first two terms
[tex]\sqrt[3]{2x}(7-6)-6\sqrt[3]{x}[/tex]
[tex]\sqrt[3]{2x}-6\sqrt[3]{x}[/tex]
Therefore, The simplified form of the expression is [tex]\sqrt[3]{2x}-6\sqrt[3]{x}[/tex]
