Let's analyze the given values for the square roots of numbers to draw some conclusions about the square roots of numbers greater than 2.
Here are the values provided:
[tex]\[
\begin{array}{l}
\sqrt{2}=1.4 \\
\sqrt{3}=1.7 \\
\sqrt{4}=2.0 \\
\sqrt{5}=2.2
\end{array}
\][/tex]
### Step-by-Step Analysis:
1. Square Root of 2:
[tex]\(\sqrt{2}\)[/tex] is given as 1.4. This is our reference value for the square root of 2.
2. Square Root of 3:
[tex]\(\sqrt{3}\)[/tex] is given as 1.7. We observe that:
[tex]\[
\sqrt{3} > \sqrt{2} \implies 1.7 > 1.4
\][/tex]
This shows that the square root of 3 is greater than the square root of 2.
3. Square Root of 4:
[tex]\(\sqrt{4}\)[/tex] is given as 2.0. We observe that:
[tex]\[
\sqrt{4} > \sqrt{2} \implies 2.0 > 1.4
\][/tex]
And also:
[tex]\[
\sqrt{4} > \sqrt{3} \implies 2.0 > 1.7
\][/tex]
This shows that the square root of 4 is greater than both the square roots of 2 and 3.
4. Square Root of 5:
[tex]\(\sqrt{5}\)[/tex] is given as 2.2. We observe that:
[tex]\[
\sqrt{5} > \sqrt{2} \implies 2.2 > 1.4
\][/tex]
And also:
[tex]\[
\sqrt{5} > \sqrt{3} \implies 2.2 > 1.7
\][/tex]
And also:
[tex]\[
\sqrt{5} > \sqrt{4} \implies 2.2 > 2.0
\][/tex]
This shows that the square root of 5 is greater than the square roots of 2, 3, and 4.
### Conclusion:
From the above observations:
- [tex]\(\sqrt{3}\)[/tex], [tex]\(\sqrt{4}\)[/tex], and [tex]\(\sqrt{5}\)[/tex] are each greater than [tex]\(\sqrt{2}\)[/tex].
- The square root values increase as the numbers increase.
Therefore, we can conclude:
- The square root of numbers greater than 2 is always greater than the square root of 2.
- Additionally, with the provided rounded values, the exact square root values would be slightly higher than the provided estimates.
In summary, the square root of any number greater than 2 is greater than 1.4 (the square root of 2), and the trend is an increasing function as observed in the given values.
