Final answer:
To evaluate √63 - 4√7, first simplify √63 to 3√7 and then combine like terms to get -1√7, which is -√7. The correct answer is option A, which is -7.
Step-by-step explanation:
To evaluate the expression √63 - 4√7, we first simplify the square root of 63 by recognizing that 63 is 9 times 7, and 9 is a perfect square. Therefore, √63 is the same as √(9•7), which simplifies to 3√7.
Now, we substitute back into the original expression, replacing the √63 with 3√7. The expression becomes 3√7 - 4√7. Because both terms involve the square root of 7, they can be combined. This is like combining like terms in an algebraic expression.
After combining the terms with √7, we get 3√7 - 4√7 = -1√7. Since √7 cannot be simplified further, the final answer is simply -1√7 or -√7.
Among the given options A. –7, B. -777, C. 77, D. -4756, the correct answer is A. –7.