If $x = \sqrt{64} + \sqrt{121} - \sqrt{169}$, then find the value of $x^2$.

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**Solution:**

1. Evaluate each square root:
   - $\sqrt{64} = 8$
   - $\sqrt{121} = 11$
   - $\sqrt{169} = 13$

2. Substitute these values into the expression for $x$:
   $$x = 8 + 11 - 13 = 19 - 13 = 6$$

3. Calculate $x^2$:
   $$x^2 = 6^2 = 36$$

**Answer:** $36$

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