Find the two consecutive whole numbers the square root is between. Explain. √(39)√(600)

Question

Find the two consecutive whole numbers the square root is between. Explain.
`√(39)`
`√(600)`

Answer 1

1) First notice that we have the following expressions that are always true:

`\begin{gathered} \sqrt[]{36}=6 \\ \sqrt[]{49}=7 \end{gathered}`

We also know that:

`36<39<49`

Using square root on the whole equality we get:

`\begin{gathered} \sqrt[]{36}<\sqrt[]{39}<\sqrt[]{49} \\ \Rightarrow6<\sqrt[]{39}<7 \end{gathered}`

therefore, the square root of 39 is between 6 and 7.

2)for the square root of 600, we have the following:

`\begin{gathered} 600<625 \\ \text{ using square root on both sides:} \\ \sqrt[]{600}<\sqrt[]{625}=25 \\ \Rightarrow\sqrt[]{600}<25 \end{gathered}`

since the square root of 625 is the minimum number that has an integer as a solution, we have that the square root of 600 is between 24 and 25