Question

Determine whether the given number is an irrational number or a rational number and place it in its representing category
`√(120)`
`√(36)`
`\sqrt[7]{16}`
`√(48)`
`√(81)`
`\pi`

Answer 1

An irrational number could not be written as a fraction.

We need to clasify the following numbers in rational or irrational:

`\begin{gathered} \sqrt[]{120}=\sqrt[]{4\cdot30}=2\cdot\sqrt[]{30}\Rightarrow Is\text{ irrational because }\sqrt[]{30}\text{ is irrational} \\ \sqrt[]{36}=6\Rightarrow Is\text{ rational} \\ \sqrt[7]{16}\Rightarrow\text{ Is irrational} \\ \sqrt[]{48}=\sqrt[]{16\cdot3}=4\cdot\sqrt[]{3}\Rightarrow Is\text{ irrational because }\sqrt[]{3}\text{ is irrational} \\ \sqrt[]{81}=9\Rightarrow Is\text{ rational} \\ \pi\text{ is irrational} \end{gathered}`