Question

(9 - square root 2)squared

Answer 1

To simplify \((9 - \sqrt{2})^2\), we can use the formula \((a - b)^2 = a^2 - 2ab + b^2\).

Here, \(a = 9\) and \(b = \sqrt{2}\).

Now let's calculate it step by step:

1. Calculate \(a^2\):
\[
9^2 = 81
\]

2. Calculate \(2ab\):
\[
2 \cdot 9 \cdot \sqrt{2} = 18\sqrt{2}
\]

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

Now we can put it all together:
\[
(9 - \sqrt{2})^2 = 81 - 18\sqrt{2} + 2
\]
Combine the constant terms:
\[
81 + 2 = 83
\]

So, the final result is:
\[
(9 - \sqrt{2})^2 = 83 - 18\sqrt{2}
\]