To address the given expression [tex]\( 4 \sqrt{2} - 5 \sqrt{3} \)[/tex], let's go through each option one by one:
A. The two terms cannot be combined because the radicands are not identical, and cannot be simplified so that they are identical.
- This statement suggests that because [tex]\( \sqrt{2} \)[/tex] and [tex]\( \sqrt{3} \)[/tex] have different values under the radical sign (radicands), and these values cannot be changed to become the same, the terms cannot be combined.
- Correct. Since the radicands ([tex]\( 2 \)[/tex] and [tex]\( 3 \)[/tex]) are not the same, these terms cannot be combined.
B. The two terms cannot be combined because the indices are not identical.
- This statement would be relevant if we had different indices (such as [tex]\(\sqrt[3]{2}\)[/tex] and [tex]\(\sqrt{3}\)[/tex]), but in this case, both terms are square roots, so the indices are indeed the same.
- Incorrect. The indices for both terms in [tex]\( 4 \sqrt{2} - 5 \sqrt{3} \)[/tex] are the same (both are square roots).
C. The two terms cannot be combined because the resulting value of the subtraction would be negative.
- This statement is incorrect because combining terms based on whether the result is negative or positive doesn’t affect whether they can be combined or not.
- Incorrect. The possibility of a negative result does not factor into whether the terms can be combined in this algebraic context.
D. The two terms may be combined.
- This statement is suggesting that it is possible to combine the terms [tex]\( 4 \sqrt{2} \)[/tex] and [tex]\( 5 \sqrt{3} \)[/tex].
- Incorrect. We cannot combine these terms directly because their radicands are not the same.
Therefore, the best answer from the given choices is:
A. The two terms cannot be combined because the radicands are not identical, and cannot be simplified so that they are identical.
