To solve the equation \( x^2 = 1625 \) by inspection, we first find the square root of 1625.
Calculating the square root:
\[ x = \sqrt{1625} \quad \text{and} \quad x = -\sqrt{1625} \]
Next, we simplify \( \sqrt{1625} \). We can factor 1625:
\[ 1625 = 25 \times 65 = 25 \times 5 \times 13 \]
Taking the square root:
\[ \sqrt{1625} = \sqrt{25 \times 65} = \sqrt{25} \times \sqrt{65} = 5\sqrt{65} \]
Thus, the two real solutions are:
\[ x = 5\sqrt{65} \quad \text{and} \quad x = -5\sqrt{65} \]
To present the answers in simplest fraction form, we note that \( 5\sqrt{65} \) is already in its simplest form, as is \( -5\sqrt{65} \).
The lesser number should come first:
\[ -5\sqrt{65}, , 5\sqrt{65} \]
So, the final solutions are:
\[ \boxed{-5\sqrt{65}, , 5\sqrt{65}} \]
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