Question 11

2√3

The expression (4 + √7)(8 - √28) simplifies to a value that is closest to 2√3 when divided by 3√2.

A) 2√3

This option is correct as the simplified form of the given expression indeed evaluates to 2√3 after performing the necessary calculations and simplifications.

B) 25

This option is incorrect because the result of the expression is not an integer like 25. Given that the expression involves square roots, the output cannot be a whole number, making this option invalid.

C) 3√5

This option is also incorrect. Although it is a radical expression, it does not match the simplified form of the calculation. The coefficients and the radical component do not correlate with the final value derived from the original expression.

D) 2√6

This option is incorrect as well. The value 2√6 is not close to the correct answer derived from the expression. The calculation does not yield this particular radical form, thus making it an unsuitable choice.

Conclusion

The correct answer of 2√3 accurately represents the simplified form of the expression when calculated correctly. All other options fail to match the result either by being whole numbers or by not aligning with the radical formats derived from the expression. Hence, 2√3 stands as the only valid solution among the choices provided.