Solve x2=25/64

Question

by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

Answer 1

To solve the equation \( x^2 = \frac{25}{64} \) by inspection, we can take the square root of both sides.

1. Take the square root of both sides:

\[ x = \pm \sqrt{\frac{25}{64}} \]

2. Calculate the square root:

\[ \sqrt{\frac{25}{64}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8} \]

3. Therefore, the two real solutions are:

\[ x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8} \]

4. Entering the lesser number first, we have:

\[ -\frac{5}{8}, \frac{5}{8} \]

Thus, the solutions are:

\[

• \frac{5}{8}, \frac{5}{8} \]