Question

The area formula for rectangular shapes is A=LW. What is the area of a rectangular shape with the dimensions of
`\sqrt[4]{11}` and
`\sqrt[4]{3}`?

Answer 1

`\textsf{area}=\sqrt[4]{33}\:\textsf{square units}`

Explanation:

Formula

Area of a rectangle = length × width

Given:

• 
  `\textsf{length}=\sqrt[4]{11}`
• 
  `\textsf{width}=\sqrt[4]{3}`

Substitute given values into the formula:

`\implies \textsf{area}=\sqrt[4]{11} \cdot \sqrt[4]{3}`

`\textsf{Apply radical rule}\quad\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}:`

`\implies \textsf{area}=\sqrt[4]{11 \cdot 3} =\sqrt[4]{33}\:\textsf{square units}`

Answer 2

Hi!

Given the area formula ~ A = LW

We need to multiply the two values:

`\sqrt[4]{11} * \sqrt[4]{3}`

Since they have the same root, 4, we can multiply what's inside of the radical and give it the same root.

`11*3=33`

Now, we apply the same root as before:

`\sqrt[4]{33}`

Therefore, your answer is
`\sqrt[4]{33}`

Now, if you need that as a numerical value rather than a radical, it's roughly
`2.397`