Final answer:
The student's mathematical expression 11√45 - 4.5 simplifies to 33√5 - 4.5 which cannot be further simplified. None of the given options represents the simplified form of the expression correctly. The correct option is 2.
Step-by-step explanation:
The student has asked to calculate the following mathematical expression: 11√45 - 4.5. To simplify and find the difference, we first need to simplify the square root term.
Let's simplify √45 by recognizing that 45 can be factored into 9 × 5, and since 9 is a perfect square, we can take its square root out of the radical:
- √45 = √(9 × 5) = √9 × √5 = 3√5
Now, we rewrite the original expression using this simplification:
- 11√45 - 4.5 = 11(3√5) - 4.5
- = 33√5 - 4.5
We can't simplify any further because one term contains a radical, and the other does not. The difference remains in this form unless the question implies a numerical approximation, in which case we should calculate and possibly round the result as per instruction.
However, among the answer options, there is one that matches our expression:
Recognizing that √10 is just 2 times √5, we can rewrite this option as follows:
- 14√10 = 14(2√5) = 28√5
- Which is not equal to 33√5 - 4.5
So none of the provided options correctly represents the simplified form of the original expression. The correct option is 2.