To solve the equation
\[ x^2 = \dfrac{36}{49}, \]
we take the square root of both sides. When taking the square root, we consider both the positive and negative solutions:
\[ x = \pm \sqrt{\dfrac{36}{49}}. \]
We can simplify the square root:
\[ x = \pm \dfrac{\sqrt{36}}{\sqrt{49}} = \pm \dfrac{6}{7}. \]
This gives us the two solutions:
\[ x = \dfrac{6}{7} \quad \text{and} \quad x = -\dfrac{6}{7}. \]
Now let's examine the given choices:
- (Choice A) \(x = \dfrac{\sqrt{36}}{\sqrt{49}}\) simplifies to \(x = \dfrac{6}{7}\). This is correct.
- (Choice B) \(x = -\dfrac{6}{7}\) is correct.
- (Choice C) \(x = \dfrac{\sqrt{36}}{13}\) simplifies to \(x = \dfrac{6}{13}\), which does not match our solutions. This is incorrect.
- (Choice D) \(x = -\dfrac{6}{13}\). This also does not match our solutions. This is incorrect.
- (Choice E) None of the above. Since we have correct choices A and B, this is incorrect.
Thus, the correct choices are:
- Choice A: \(x = \dfrac{6}{7}\)
- Choice B: \(x = -\dfrac{6}{7}\)
Final answer:
- (Choice A) and (Choice B) are correct.