Question

to plot the square roots on a number line for the purpose of comparison, we first need to estimate the approximate numbers to the ____________ place that the square root is between

3^2< 11 <__

√11 is between 3.3 and ____ 3.4^2=____

Answer 1

To find the square root of 11 and estimate its approximate value for plotting on a number line, we can start with identifying perfect squares around number 11.

First, we know that:

\[
3^2 = 9 < 11 < 16 = 4^2
\]

This tells us that the square root of 11 is between 3 and 4.

To narrow it down further, we can calculate the squares of numbers between 3 and 4. We can start with 3.3 and 3.4.

Calculating \(3.3^2\):

\[
3.3^2 = 10.89
\]

Calculating \(3.4^2\):

\[
3.4^2 = 11.56
\]

Now, we see that:

\[
10.89 < 11 < 11.56
\]

Thus, we have:

\[
\sqrt{11} \text{ is between } 3.3 \text{ and } 3.4.
\]

So, filling in the blanks:

3^2 < 11 < 4^2
√11 is between 3.3 and **3.4**
3.4^2 = **11.56**

This gives us a clearer comparison for plotting on the number line!