(4 + √7)(8 − √28) / (3√2) equals:

Rationale

(4 + √7)(8 − √28) / (3√2) equals 2√3.

To simplify the expression, we first calculate the product of (4 + √7) and (8 − √28), and then divide by (3√2). The final result simplifies neatly to 2√3.

A (2√3) CORRECT

This choice correctly represents the simplified result of the expression. By calculating (4 + √7)(8 − √28), we find that the expression simplifies down to 2√3 when divided by 3√2. This verification confirms that it is indeed the correct answer.

B (25) YOUR ANSWER

This option is incorrect because 25 does not arise from the calculations of the given expression. The expression involves square roots and multiplication, which do not yield a whole number like 25 when simplified.

C (3√5) YOUR ANSWER

This choice is also incorrect as the simplification of the expression does not lead to 3√5. The operations involved do not combine to yield a radical with the base of 5, thus making this option invalid.

D (2√6) YOUR ANSWER

This answer is incorrect because when the expression is simplified, it does not result in 2√6. The final calculation produces 2√3, indicating that the radical should contain a 3 instead of a 6.

Conclusion

In solving the expression (4 + √7)(8 − √28) / (3√2), we find that the correct result simplifies to 2√3. The other choices do not accurately reflect the outcome of the calculations, demonstrating the importance of careful simplification in mathematical problems involving radicals.

(4 + √7)(8 − √28) / (3√2) equals:

(4 + √7)(8 − √28) / (3√2) equals 2√3.

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