Question

What is the number of units produced if there are 625 unts of labour and 1024

Answer 1

Problem Statement

We are asked to simplify the following expression:

`4\sqrt[]{3}*2\sqrt[]{18}`

Solution

- To solve this question, we need to separate the radicals from the integers.

- Multiply the integers and the radicals separately.

- The laws of indices we shall apply to multiply the radicals are:

`\sqrt[]{a}*\sqrt[]{b}=\sqrt[]{a* b}`

- Thus, we can proceed to solve the question as follows:

`\begin{gathered} 4\sqrt[]{3}*2\sqrt[]{18} \\ \text{Separate the integers and the radicals} \\ 4*2*\sqrt[]{3}*\sqrt[]{18} \\ \text{ Multiply them out as follows} \\ (4*2)*(\sqrt[]{3}*\sqrt[]{18}) \\ =8*\sqrt[]{3*18} \\ =8*\sqrt[]{3*2*9} \\ =8*\sqrt[]{6*9} \\ =8*3\sqrt[]{6} \\ =24\sqrt[]{6} \end{gathered}`

Final Answer

`24\sqrt[]{6}`