Let's evaluate each statement to determine which are true.
1. Evaluate [tex]$\sqrt{1.8}$[/tex] and [tex]$\sqrt{1.9}$[/tex]:
- The value of [tex]$\sqrt{1.8}$[/tex] is approximately 1.3416407864998738.
- The value of [tex]$\sqrt{1.9}$[/tex] is approximately 1.378404875209022.
Now, let's check each statement one by one.
2. Statement: [tex]$\sqrt{1.8} < 1.8$[/tex]
- Comparatively, 1.3416407864998738 (which is [tex]$\sqrt{1.8}$[/tex]) is less than 1.8.
- Therefore, this statement is true.
3. Statement: [tex]$\sqrt{1.8} > 1$[/tex]
- Comparatively, 1.3416407864998738 (which is [tex]$\sqrt{1.8}$[/tex]) is greater than 1.
- Therefore, this statement is true.
4. Statement: [tex]$\sqrt{1.8} < \sqrt{1.9}$[/tex]
- Comparatively, 1.3416407864998738 (which is [tex]$\sqrt{1.8}$[/tex]) is less than 1.378404875209022 (which is [tex]$\sqrt{1.9}$[/tex]).
- Therefore, this statement is true.
5. Statement: [tex]$1.3 < \sqrt{1.8} < 1.4$[/tex]
- Comparatively, 1.3416407864998738 (which is [tex]$\sqrt{1.8}$[/tex]) lies between 1.3 and 1.4.
- Therefore, this statement is true.
6. Statement: [tex]$\sqrt{1.9} + \sqrt{1.8} > 2$[/tex]
- The sum of 1.378404875209022 (which is [tex]$\sqrt{1.9}$[/tex]) and 1.3416407864998738 (which is [tex]$\sqrt{1.8}$[/tex]) is approximately 2.7200456617088958, which is greater than 2.
- Therefore, this statement is true.
7. Statement: [tex]$\sqrt{1.9} - \sqrt{1.8} > 0.1$[/tex]
- The difference between 1.378404875209022 (which is [tex]$\sqrt{1.9}$[/tex]) and 1.3416407864998738 (which is [tex]$\sqrt{1.8}$[/tex]) is approximately 0.03676408870914816, which is less than 0.1.
- Therefore, this statement is false.
Based on the evaluations above, the true statements are:
1. [tex]$\sqrt{1.8} < 1.8$[/tex]
2. [tex]$\sqrt{1.8} > 1$[/tex]
3. [tex]$\sqrt{1.8} < \sqrt{1.9}$[/tex]
4. [tex]$1.3 < \sqrt{1.8} < 1.4$[/tex]
5. [tex]$\sqrt{1.9} + \sqrt{1.8} > 2$[/tex]
