To find the solutions to the equation
\[ b^2 = \dfrac{16}{121}, \]
we take the square root of both sides. Remember that when we take the square root, we need to consider both the positive and the negative roots. Thus, we have:
\[ b = \pm \sqrt{\dfrac{16}{121}}. \]
Calculating the square root, we find:
\[ b = \pm \dfrac{\sqrt{16}}{\sqrt{121}} = \pm \dfrac{4}{11}. \]
This results in two possible solutions:
\[ b = \dfrac{4}{11} \quad \text{and} \quad b = -\dfrac{4}{11}. \]
Now let's look at the answer choices:
- (Choice A) \(b = \dfrac{2}{7}\)
- (Choice B) \(b = -\dfrac{2}{7}\)
- (Choice C) \(b = \dfrac{4}{11}\)
- (Choice D) \(b = -\dfrac{4}{11}\)
- (Choice E) None of the above
The correct answers are:
- (Choice C) \(b = \dfrac{4}{11}\)
- (Choice D) \(b = -\dfrac{4}{11}\)
Thus, the solutions to the equation are:
(Choice C) and (Choice D).