Compute (4 + √7)(8 − √28) and choose the closest simplified form.
2√3 is the closest simplified form of the expression.
To solve the given expression, we first simplify the components: (4 + √7)(8 - √28) and then divide by (3√2), which ultimately leads to the result of 2√3.
This choice is obtained by properly simplifying the expression step-by-step. First, calculate (4 + √7)(8 - √28). Here, √28 simplifies to 2√7, making the expression (4 + √7)(8 - 2√7). Upon expanding and further simplifying, then dividing by (3√2), the resulting value simplifies down to 2√3.
The value of 25 does not emerge from the simplification process of the original expression. It overlooks the radical components and arithmetic operations involved, leading to a miscalculation that fails to recognize the necessity of maintaining the roots in the final answer.
3√5 is not a solution from the simplification of the given expression. This choice misrepresents the outcome by inaccurately combining numerical values and radicals, disregarding the correct arithmetic steps and simplifications needed to arrive at the final answer.
The option 2√6 suggests an incorrect simplification, as it does not accurately reflect the outcome of the operations performed in the expression. This choice miscalculates the factors involved, leading to a result that diverges from the correct simplification process and ultimately does not equal the expression's value.
In conclusion, the expression (4 + √7)(8 - √28) divided by (3√2) simplifies to 2√3, making it the correct answer. The other options either stem from miscalculations or incorrect interpretations of the radical simplifications, highlighting the importance of precise arithmetic operations in reaching the correct solution.
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