Question

(-8 + square root 65)squared

Answer 1

To simplify \((-8 + \sqrt{65})^2\), we can use the binomial expansion \( (a + b)^2 = a^2 + 2ab + b^2 \).

Here, \( a = -8 \) and \( b = \sqrt{65} \).

Now let's calculate each term:

1. **Calculate \( a^2 \)**:
\[
(-8)^2 = 64
\]

2. **Calculate \( 2ab \)**:
\[
2 \times (-8) \times \sqrt{65} = -16\sqrt{65}
\]

3. **Calculate \( b^2 \)**:
\[
(\sqrt{65})^2 = 65
\]

Now, putting it all together:
\[
(-8 + \sqrt{65})^2 = 64 - 16\sqrt{65} + 65
\]

Combine the constant terms \( 64 \) and \( 65 \):
\[
64 + 65 = 129
\]

Thus, the final expression is:
\[
(-8 + \sqrt{65})^2 = 129 - 16\sqrt{65}
\]