Find the solution for x when $$ x^{2}=\frac{16}{49} $$. A $$ x=\frac{4}{7} $$ B $$ x=\left(\frac{4}{7}\right)^{2} $$ C $$ x= \pm \frac{4}{7} $$ D $$ x=\left( \pm \frac{4}{7}\right)^{2} $$

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1. We start with the equation:
   $$
   x^2 = \frac{16}{49}
   $$

2. To solve for $$ x $$, we take the square root of both sides:
   $$
   \sqrt{x^2} = \sqrt{\frac{16}{49}}
   $$

3. Recall that:
   $$
   \sqrt{x^2} = |x|
   $$
   and
   $$
   \sqrt{\frac{16}{49}} = \frac{4}{7}
   $$

4. Thus, we have:
   $$
   |x| = \frac{4}{7}
   $$

5. This means that:
   $$
   x = \frac{4}{7} \quad \text{or} \quad x = -\frac{4}{7}
   $$

6. The complete solution for $$ x $$ is:
   $$
   x = \pm \frac{4}{7}
   $$

The correct answer is option C.
The solution for $$ x $$ is $$ x = \pm \frac{4}{7} $$, so the correct choice is C.

Find the solution for x when \( x^{2}=\frac{16}{49} \). A \( x=\frac{4}{7} \) B \( x=\left(\frac{4}{7}\right)^{2} \) C \( x= \pm \frac{4}{7} \) D \( x=\left( \pm \frac{4}{7}\right)^{2} \)

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