Solve x^2 = 16/25 by inspection. Tell the answers in simplest fraction form

Answer 1

To solve the equation \( x^2 = \frac{16}{25} \) by inspection, we can take the square root of both sides.

1. Recognize that \( \frac{16}{25} \) is a perfect square since \( 16 = 4^2 \) and \( 25 = 5^2 \).
2. Therefore, the square root of \( \frac{16}{25} \) can be found by taking the square roots of the numerator and denominator separately:

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

Thus, the solutions for \( x \) are

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

In simplest fraction form, the answers are:

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