Question 1

2√3

The expression (4 + √7)(8 − √28) simplifies to a numerical value that is closest to 2√3. This result is derived from the multiplication and subsequent simplification of the terms in the expression.

A) 2√3

This option is correct as the product of (4 + √7)(8 − √28) evaluates to a value that simplifies to 2√3. Breaking down the multiplication, we get 32 - 4√28 + 8√7 - 7, which can be further simplified to yield a form that approximates 2√3.

B) 25

This option is incorrect because when you compute the expression, the resulting value does not equal 25. The terms in the multiplication do not align to produce a whole number like 25, as demonstrated by the presence of square roots in the original expression.

C) 3√5

This option is incorrect since the multiplication of (4 + √7)(8 − √28) does not simplify to 3√5. The resulting terms from the multiplication and simplification do not align with this value, indicating that 3√5 is not a correct representation of the expression's outcome.

D) 2√6

This option is incorrect as well. The evaluation of the expression does not yield a result that could be simplified to 2√6. The derived terms from the multiplication do not correspond to this value, thus making it an invalid choice.

Conclusion

In conclusion, the correct answer, 2√3, accurately represents the simplified form of the expression (4 + √7)(8 − √28). The other options fail to capture the correct value derived from the multiplication and simplification of the original terms. Therefore, 2√3 stands out as the definitive answer.