Let's examine each statement one by one using our mathematical knowledge:
1. [tex]\(\sqrt{49} > 7\)[/tex]:
- [tex]\(\sqrt{49}\)[/tex] equals 7 because 49 is a perfect square (i.e., [tex]\(7^2 = 49\)[/tex]).
- This statement can be rewritten as [tex]\(7 > 7\)[/tex], which is not true.
2. [tex]\(\sqrt{48} < \(\sqrt{36}\)[/tex]:
- We know that [tex]\(\sqrt{48}\)[/tex] is around 6.93 (since [tex]\(\sqrt{49}\)[/tex] is 7 and 48 is slightly less than 49).
- We also know that [tex]\(\sqrt{36} = 6\)[/tex] since 36 is a perfect square ([tex]\(6^2 = 36\)[/tex]).
- This statement would then be comparing approximately 6.93 < 6, which is not true.
3. [tex]\(\sqrt{48} > \(\sqrt{36}\)[/tex]:
- Again, [tex]\(\sqrt{48}\)[/tex] is approximately 6.93.
- [tex]\(\sqrt{36}\)[/tex] is exactly 6.
- This statement can be rewritten as 6.93 > 6, which is true.
4. [tex]\(\sqrt{49} < 7\)[/tex]:
- As we discussed earlier, [tex]\(\sqrt{49} = 7\)[/tex].
- This statement implies [tex]\(7 < 7\)[/tex], which is not true.
So, after examining each statement, the true statement is:
[tex]\(\sqrt{48} > \(\sqrt{36}\)[/tex]
Therefore, the correct answer is statement 3.
