Question

8 - Arrange from LEAST to GREATEST without the use of a calculator

Answer 1

Given the numbers:

`3^{(1)/(3)},\text{ }4^{(1)/(2)},\text{ }\sqrt[3]{9},\text{ 1}^8,\text{ \lparen-}(1)/(2))^(-2)`

Let's arrange the numbers from the least to the greatest without the use of a calculator.

Now, let's first simplify each term.

We have:

`\begin{gathered} 3^{(1)/(3)}=\sqrt[3]{3} \\ \\ 4^{(1)/(2)}=√(4)=2 \\ \\ \sqrt[3]{9} \\ \\ 1^8=1 \\ \\ -((1)/(2))^(-2)=(-2)^2=4 \end{gathered}`

Therefore, arranging the numbers from the least to the greatest, we have:

`\begin{gathered} 1 \\ \\ \\ 3^{(1)/(3)} \\ \\ \\ 4^{(1)/(2)} \\ \\ \sqrt[3]{9} \\ \\ \\ (-(1)/(2))^(-2) \end{gathered}`