Solve x2=1625

Question

by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form. (1 point)
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Remaining Attempts : 3

Answer 1

To solve the equation \( x^2 = 1625 \) by inspection, we can take the square root of both sides.

The square roots of 1625 are:

\[ x = \sqrt{1625} \quad \text{and} \quad x = -\sqrt{1625} \]

Now, let's simplify \( \sqrt{1625} \):

1. Factor 1625: \( 1625 = 25 \times 65 = 25 \times (5 \times 13) \).
2. So, \( 1625 = 25 \times 5 \times 13 \).
3. We know \( \sqrt{25} = 5 \), thus: \[ \sqrt{1625} = \sqrt{25 \times 65} = \sqrt{25} \times \sqrt{65} = 5\sqrt{65} \]

Thus the two solutions for \( x \) are:

\[ x = 5\sqrt{65} \quad \text{and} \quad x = -5\sqrt{65} \]

To enter the answers in the requested format, we provide the lesser number first:

\[ {-5\sqrt{65}, 5\sqrt{65}} \]