Question

An experienced landscaper thought it would be funny to play a joke on some rookie landscapers. The rookies were given the measurements, l e n g t h equals 4 space cube root of 24 f t space a n d space w i d t h equals 6 space cube root of 3 space f t , and asked to find the exact area (no decimals) of the rectangular region they would be working with. Show the equation and all work needed to find the exact area in simplest form. Be sure to write a sentence explaining your answer. Don’t forget the label! Note: we want the exact area, which is not a decimal. Instead, provide the answer in simplest radical form.

Answer 1

48∛9 ft²

Explanation:

The length (L) and width (W) are given by:

`L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}`

Since this is a rectangular region, the area is given by:

`A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2`

The answer can be further simplified by factoring as follows:

`A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2`

The exact area is its simplest form is 48∛9 ft²