Expand the expression using the formula (a-b)^2 = a^2 - 2ab + b^2.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Expand the expression using the formula $(a-b)^2 = a^2 - 2ab + b^2$.
Here, $a = \sqrt{7}$ and $b = 6$.
$$(\sqrt{7}-6)^2 = (\sqrt{7})^2 - 2(\sqrt{7})(6) + (6)^2$$
Step 2: Perform the squaring and multiplication operations.
$$= 7 - 12\sqrt{7} + 36$$
Step 3: Combine the constant terms.
$$= (7 + 36) - 12\sqrt{7}$$
$$= 43 - 12\sqrt{7}$$
The answer in surd form is:
$$\boxed{43 - 12\sqrt{7}}$$
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