Question: Find the foci of this hyperbola.
$$\frac{x^2}{52} - \frac{y^2}{20} = 1$$
Foci = $(\pm[?]\sqrt{[ ]}, 0)$
Simplify your answer completely.
1. **State the problem:** Find the foci of the hyperbola given by the equation $$\frac{x^2}{52} - \frac{y^2}{20} = 1$$.
2. **Identify the form and parameters:** This is a horizontal hyperbola centered at the origin with the standard form $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$.
Here, $$a^2 = 52$$ and $$b^2 = 20$$.
3. **Recall the formula for the foci of a horizontal hyperbola:** The foci are located at $$\left(\pm c, 0\right)$$ where $$c = \sqrt{a^2 + b^2}$$.
4. **Calculate $$c$$:**
$$
c = \sqrt{a^2 + b^2} = \sqrt{52 + 20} = \sqrt{72}
$$
5. **Simplify $$\sqrt{72}$$:**
$$
\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
$$
6. **Write the coordinates of the foci:**
$$
(\pm 6\sqrt{2}, 0)
$$
**Final answer:** The foci of the hyperbola are at $$\boxed{(\pm 6\sqrt{2}, 0)}$$.