Question

Which of the following numbers are greater than 6 and less than 8?

Answer 1

`√(60)`

Step-by-step explanation:

We are required to determine which of the given numbers are greater than 6 and less than 8.

`6^2=36\text{ and }8^2=64`
`\begin{gathered} √(7)<√(36)=6 \\ \text{Therefore, }√(7)\text{ is less than 6.} \end{gathered}`

Secondly:

`\begin{gathered} 6=√(36)<√(60)<√(64)=8 \\ 6<√(60)<8 \\ \text{Therefore, }√(60)\text{ is greater than 6 and less than 8.} \end{gathered}`

Finally:

`\begin{gathered} 6=√(36)<√(80)>√(64)=8 \\ √(80)>8>6 \\ \text{Therefore, }√(80)\text{ is greater than 6 and 8.} \end{gathered}`

Therefore, the number which is greater than 6 and less than 8 is the square root of 60.