To solve the equation \( x^2 = 1625 \) by inspection, we need to find the values of \( x \) that satisfy the equation.
Taking the square root of both sides gives:
\[ x = \pm \sqrt{1625} \]
Next, we can simplify \( \sqrt{1625} \):
First, we can factor 1625: \[ 1625 = 25 \times 65 \] Since \( 25 = 5^2 \), we can further simplify: \[ \sqrt{1625} = \sqrt{25 \times 65} = \sqrt{25} \times \sqrt{65} = 5\sqrt{65} \]
Therefore, the solutions for \( x \) are: \[ x = 5\sqrt{65} \quad \text{and} \quad x = -5\sqrt{65} \]
So the two real solutions are: \(-5\sqrt{65}\) and \(5\sqrt{65}\).
In simplest fraction form, the answers can be written as: \[ -\frac{5\sqrt{65}}{1} \quad \text{and} \quad \frac{5\sqrt{65}}{1} \]
Thus, the final answers are: \[ -5\sqrt{65}, ; 5\sqrt{65} \]
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