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

Sagot :

Use the properties of radicals to rewrite the numbers.

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

It is a known fact that:

[tex]1<\sqrt[]{2}[/tex]

Multiply both sides of the inequality by 2:

[tex]2<2\cdot\sqrt[]{2}[/tex]

Substitute for √8=2√2 and √16/2=2:

[tex]\frac{\sqrt[]{16}}{2}<\sqrt[]{8}[/tex]

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