Question

Simplify the following
`\sqrt[3]{343 } + (3)/(4) \sqrt[3]{ - 8}`

Answer 1

`\sqrt[3]{343}+(3)/(4)\sqrt[3]{-8}\text{ =}(11)/(2)`

Step-by-step explanation

The cube root of a number is the factor that we multiply by itself three times to get that number

so

Step 1

`\sqrt[3]{343}+(3)/(4)\sqrt[3]{-8}`
`\begin{gathered} \sqrt[3]{343}\text{ =7} \\ because,\cdot7\cdot7\cdot7=343 \\ \end{gathered}`

and

`\begin{gathered} \sqrt[3]{-8}\text{ =-2} \\ \text{because -2}\cdot-2\cdot-2=-8 \end{gathered}`

Step 2

replace

`\begin{gathered} \sqrt[3]{343}+(3)/(4)\sqrt[3]{-8} \\ 7+(3)/(4)(-2)=7-(6)/(4)=(28-6)/(4)=(22)/(4)=(11)/(2) \end{gathered}`

so,the answer is

`\sqrt[3]{343}+(3)/(4)\sqrt[3]{-8}\text{ =}(11)/(2)`

I hope this helps you