Question

What's the inverse operation of a cubing number?Also, can you please solve and explain this examples?

Answer 1

The inverse of cubing a number is applying cubic root

`a^3\leftrightarrow\sqrt[3]{a}`

Now, let's go through the examples:

When you want to find the square root of a number x you have to ask yourself:

Which number, when multiplied by itself, will give me x ?

For example,

`\sqrt[]{225}=15`

Because

`\begin{gathered} 15*15=225 \\ 15^2=225 \end{gathered}`

This way,

`\begin{gathered} \sqrt[]{49}=7\Leftrightarrow7^2=49 \\ \sqrt[]{121}=11\Leftrightarrow11^2=121 \\ \sqrt[]{1600}=40\Leftrightarrow40^2=1600 \end{gathered}`

Now for the cubic root:

When you want to find the cubic root of a number y you have to ask yourself:

Which number, when multiplied by itself two times, will give me y ?

For instance,

`\sqrt[3]{64}=8`

Because

`\begin{gathered} 8*8*8=64 \\ 8^3=64 \end{gathered}`

Therefore,

`\begin{gathered} \sqrt[3]{8}=2\Leftrightarrow2^3=8 \\ \sqrt[3]{1}=1\Leftrightarrow1^3=1 \\ \sqrt[3]{2744}=14\Leftrightarrow14^3=2744 \end{gathered}`