To solve the equation \( x^2 = 7^8 \), we can take the square root of both sides.
When we do so, we get:
\[ x = \pm \sqrt{7^8} \]
Using the property of exponents, we can simplify \( \sqrt{7^8} \):
\[ \sqrt{7^8} = 7^{8/2} = 7^4 \]
So, the solutions to the equation are:
\[ x = 7^4 \quad \text{and} \quad x = -7^4 \]
Thus, the two real solutions are:
- \( -7^4 \)
- \( 7^4 \)
So the correct answer is:
- \( -7^4, 7^4 \)