Solve x^2=25/64 by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

1 answer

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

Taking the square root gives:

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

This can be simplified:

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

Thus, we have two solutions:

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

When listing the solutions with the lesser number first, we get:

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

Therefore, the two real solutions are:

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