Question

Solve $x^{2}=\frac {25}{64}$ by inspection. There are two real solutions. Enter the lesser
number first. Leave the answers in simplest fraction form. (1 point)

Answer 1

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

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

We can simplify the square root:

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

Thus, the solutions to the equation are:

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

The lesser number is \( -\frac{5}{8} \) and the greater number is \( \frac{5}{8} \). Therefore, the two solutions are:

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

The final answer is:

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