Compare.

3⅔

√11

Q: Compare. 3⅔ √11

To compare $3\frac{2}{3}$ and $\sqrt{11}$, we first need to express both numbers in a form that can be easily compared. First, convert the mixed number $3\frac{2}{3}$ into an improper fraction: \[3\frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3}\] Now, we look at $\sqrt{11}$. Since $\sqrt{11}$ is an irrational number, it cannot be precisely expressed as a fraction, but we can estimate its value. We know that: \[3^2 = 9 < 11 < 16 = 4^2\] So, $\sqrt{11}$ is somewhere between 3 and 4. To get a more precise value, we can use a calculator: \[\sqrt{11} \approx 3.317\] Now, let's express $\frac{11}{3}$ as a decimal for easier comparison: \[\frac{11}{3} = 3.\overline{6}\] Comparing the two values: - $\frac{11}{3} = 3.\overline{6}$ - $\sqrt{11} \approx 3.317$ We can see that $3.\overline{6}$ (or $3.666...$) is greater than $3.317$. Therefore: \[3\frac{2}{3} > \sqrt{11}\]

Question

Compare.
 
 3⅔

√11

Accepted Answer

To compare $3\frac{2}{3}$ and $\sqrt{11}$, we first need to express both numbers in a form that can be easily compared.

First, convert the mixed number $3\frac{2}{3}$ into an improper fraction:
$$3\frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3}$$

Now, we look at $\sqrt{11}$. Since $\sqrt{11}$ is an irrational number, it cannot be precisely expressed as a fraction, but we can estimate its value. We know that:
$$3^2 = 9 < 11 < 16 = 4^2$$

So, $\sqrt{11}$ is somewhere between 3 and 4. To get a more precise value, we can use a calculator:
$$\sqrt{11} \approx 3.317$$

Now, let's express $\frac{11}{3}$ as a decimal for easier comparison:
$$\frac{11}{3} = 3.\overline{6}$$

Comparing the two values:
- $\frac{11}{3} = 3.\overline{6}$
- $\sqrt{11} \approx 3.317$

We can see that $3.\overline{6}$ (or $3.666...$) is greater than $3.317$. Therefore:
$$3\frac{2}{3} > \sqrt{11}$$

Compare. 3⅔ √11

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