The equation \( x^2 = 91 \) can be solved by taking the square root of both sides. This gives:
\[ x = \pm \sqrt{91} \]
Since 91 is not a perfect square, \( \sqrt{91} \) is an irrational number. Therefore, the equation has two solutions:
\[ x = \sqrt{91} \quad \text{and} \quad x = -\sqrt{91} \]
Thus, the correct response is:
Two irrational solutions.