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Which statements are true? Select the five correct answers.

A. [tex]\sqrt{1.8}\ \textless \ 1.8[/tex]
B. [tex]\sqrt{1.8}\ \textgreater \ 1[/tex]
C. [tex]\sqrt{1.8}\ \textless \ \sqrt{1.9}[/tex]
D. [tex]1.3\ \textless \ \sqrt{1.8}\ \textless \ 1.4[/tex]
E. [tex]\sqrt{1.9}+\sqrt{1.8}\ \textgreater \ 2[/tex]
F. [tex]\sqrt{1.9}-\sqrt{1.8}\ \textgreater \ 0.1[/tex]


Sagot :

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]