To solve for \( a \) in the equation \( a^2 = 62 \), we take the square root of both sides:
\[ a = \pm \sqrt{62} \]
Next, we can simplify \( \sqrt{62} \). The number 62 can be expressed as \( 62 = 2 \times 31 \), but neither 2 nor 31 are perfect squares, meaning \( \sqrt{62} \) cannot be simplified further.
Thus, the solution for \( a \) is:
\[ a = \pm \sqrt{62} \]