Question

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Explanation:

Step1: Identify square numbers around 11

We know that $3^2 = 9$ and $4^2 = 16$. So $\sqrt{11}$ is between 3 and 4. Now, let's check numbers with one decimal place. $3.3^2 = 10.89$, $3.4^2 = 11.56$. So $\sqrt{11}$ is between 3.3 and 3.4.

Step2: Check hundredths place

Let's calculate $3.31^2 = 3.31\times3.31 = 10.9561$, $3.32^2 = 3.32\times3.32 = 11.0224$, $3.33^2 = 3.33\times3.33 = 11.0889$. Since $11.0224$ is closer to 11 than $10.9561$ and $11.0889$, $\sqrt{11}\approx3.32$ (to the nearest hundredth).

Answer:

3.32 (and its approximate location on the number line is near 3.3, closer to 3.32)