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We are given the equation:

\[
x^2 = \frac{16}{25}
\]

To solve for \(x\), we take the square root of both sides of the equation. This will yield two solutions because both positive and negative values of \(x\) can satisfy the equation.

\[
x = \pm \sqrt{\frac{16}{25}}
\]

We can simplify the square root:

\[
x = \pm \frac{\sqrt{16}}{\sqrt{25}} = \pm \frac{4}{5}
\]

Thus, the two solutions are:

\[
x = \frac{4}{5} \quad \text{and} \quad x = -\frac{4}{5}
\]

The lesser number is \(-\frac{4}{5}\), and the greater number is \(\frac{4}{5}\).

### Final answer:
The two real solutions are \(-\frac{4}{5}\) and \(\frac{4}{5}\), with \(-\frac{4}{5}\) being the lesser.

Would you like more details or have any questions? 

Here are some follow-up questions to deepen your understanding:
1. What are the general steps to solve quadratic equations by inspection?
2. How does taking the square root of both sides introduce two possible solutions?
3. What happens if the fraction under the square root cannot be simplified easily?
4. How would the solution change if the equation were \(x^2 = -\frac{16}{25}\)?
5. What other methods could you use to solve this equation besides taking square roots?

**Tip:** Always remember to check for both positive and negative square roots when solving quadratic equations.

Solve x^2 = 16/25 by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

Learn how to solve the quadratic equation x^2 = 16/25 by inspection. This problem involves solving quadratic equations using square roots. The answer is provided in simplest fraction form, and the solution explains the process step by step. Suitable for students in Grades 7-9.

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