To solve the equation \( f^2 = 196 \), we can take the square root of both sides. Remember that taking the square root of a number gives both a positive and negative solution.
Starting with: \[ f^2 = 196 \] Taking the square root of both sides: \[ f = \pm\sqrt{196} \]
Calculating \(\sqrt{196}\): \[ \sqrt{196} = 14 \]
Thus, we have: \[ f = 14 \quad \text{or} \quad f = -14 \]
Now, let's check the choices given:
- (Choice A) \( f = 14 \) ✅
- (Choice B) \( f = -14 \) ✅
- (Choice C) \( f = 15 \) ❌
- (Choice D) \( f = -15 \) ❌
- (Choice E) None of the above ❌
The valid solutions to the equation \( f^2 = 196 \) are:
- \( f = 14 \)
- \( f = -14 \)
Therefore, the correct answers are: (Choice A) \( f = 14 \) and (Choice B) \( f = -14 \).