(4 + √(7)(8 - √(28) / (√(2) equals

Rationale

(4 + √(7))(8 - √(28)) / (3√(2)) equals 2√(3).

To solve the expression, we first simplify the radicals. Note that √(28) = 2√(7).

A (2√(3)) CORRECT

This choice is correct. Simplify the expression:
(4 + √(7))(8 - 2√(7)) = 32 - 8√(7) + 8√(7) - 14 = 18.
Then divide: 18 / (3√(2)) = 6 / √(2).
Rationalizing gives 6√(2) / 2 = 3√(2).
So the correct simplified value is 3√(2), not 2√(3).

B (25) YOUR ANSWER

This choice is incorrect because the expression simplifies to a value involving radicals, not a whole number.

C (3√(5) YOUR ANSWER

This is incorrect. The simplification results in 3√(2), not 3√(5).

D (2√(6)) YOUR ANSWER

This is also incorrect. There is no step in the simplification that leads to √(6).

Conclusion

After simplifying correctly, the expression equals 3√(2). The original claim of 2√(3) is incorrect due to an arithmetic mistake when combining like radical terms.

(4 + √(7)(8 - √(28) / (√(2) equals

(4 + √(7))(8 - √(28)) / (3√(2)) equals 2√(3).

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