To solve the equation \( x^2 = \frac{16}{25} \) by inspection, we need to find \( x \) such that when squared, it equals \( \frac{16}{25} \).
We can express \( x \) in terms of a square root:
\[ x = \pm \sqrt{\frac{16}{25}} \]
Calculating the square root of the fraction:
\[ \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5} \]
Now we consider both the positive and negative solutions:
\[ x = \frac{4}{5} \quad \text{and} \quad x = -\frac{4}{5} \]
Thus, the two solutions are:
\[ -\frac{4}{5} \quad \text{and} \quad \frac{4}{5} \]
In simplest fraction form, the lesser number first is:
\[ -\frac{4}{5}, \frac{4}{5} \]
These are the final answers.
1 answer