Question

√8 and √16/2 make an inequality expression with these 2 numbers that show how they compare.

Answer 1

Use the properties of radicals to rewrite the numbers.

`\begin{gathered} \sqrt[]{8}=\sqrt[]{4\cdot2} \\ =\sqrt[]{4}\cdot\sqrt[]{2} \\ =2\cdot\sqrt[]{2} \end{gathered}`
`\begin{gathered} \frac{\sqrt[]{16}}{2}=(4)/(2) \\ =2 \end{gathered}`

It is a known fact that:

`1<\sqrt[]{2}`

Multiply both sides of the inequality by 2:

`2<2\cdot\sqrt[]{2}`

Substitute for √8=2√2 and √16/2=2:

`\frac{\sqrt[]{16}}{2}<\sqrt[]{8}`