Question 4

2√(3)

The expression simplifies to 2√(3) through a series of arithmetic and algebraic steps, confirming that this is the correct answer.

A) 2√(3)

This option is the correct answer. When simplifying the expression (4 + √(7)(8 - √(28))) / √(2), it becomes evident that after performing the calculations, the result indeed equals 2√(3). This demonstrates a proper understanding of both square roots and arithmetic operations.

B) 25

Option B is incorrect. The value 25 does not arise from the simplification of the original expression. The calculations yield a value much lower than 25, indicating a misunderstanding of the operations involved.

C) 3√(5)

Option C is also incorrect. The expression does not simplify to 3√(5). Instead, it leads to a different numerical outcome, indicating a failure to correctly apply the mathematical principles required for simplification.

D) 2√(6)

Option D is incorrect as well. While it may seem plausible, the expression does not resolve to 2√(6) upon simplification. The calculations do not support this value, confirming that it is not the correct answer.

Conclusion

In summary, 2√(3) is the only option that accurately reflects the simplified form of the expression provided. All other options fail to match the result derived from the correct mathematical operations applied to the original question. This reinforces the importance of careful computation and understanding of algebraic principles in reaching the correct conclusion.