Question

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

Answer 1

Answer:

$\sqrt{60}$

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} \sqrt{7}<\sqrt{36}=6 \\ \text{Therefore, }\sqrt{7}\text{ is less than 6.} \end{gathered}$

Secondly:

$\begin{gathered} 6=\sqrt{36}<\sqrt{60}<\sqrt{64}=8 \\ 6<\sqrt{60}<8 \\ \text{Therefore, }\sqrt{60}\text{ is greater than 6 and less than 8.} \end{gathered}$

Finally:

$\begin{gathered} 6=\sqrt{36}<\sqrt{80}>\sqrt{64}=8 \\ \sqrt{80}>8>6 \\ \text{Therefore, }\sqrt{80}\text{ is greater than 6 and 8.} \end{gathered}$

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