Final answer:
To expand and simplify (7 + √6)^2, we apply the binomial square formula yielding 49 (7^2) + 14√6 (2× 7 ×√6) + 6 (√6^2), and by adding we obtain 55 + 14√6.
Step-by-step explanation:
To expand and simplify (7 + √6)^2, we will apply the formula (a+b)^2 = a^2 + 2ab + b^2:
- First, calculate the square of the first term: 7^2 = 49.
- Next, calculate two times the product of the two terms: 2 × 7 × √6 = 14√6.
- Then, calculate the square of the second term: (√6)^2 = 6.
- Finally, add all the results together: 49 + 14√6 + 6.
By adding the constant terms (49 and 6), we get:
49 + 6 = 55
So the expanded and simplified form of (7 + √6)^2 is 55 + 14√6.