Answer :
To solve the equation [tex]\( f^2 = 84 \)[/tex] for [tex]\( f \)[/tex], we need to find the values of [tex]\( f \)[/tex] that make this equation true.
1. Understanding the Equation: The equation [tex]\( f^2 = 84 \)[/tex] tells us that the square of [tex]\( f \)[/tex] equals 84. To find [tex]\( f \)[/tex], we will take the square root of both sides of the equation.
2. Taking the Square Root:
- When you take the square root of both sides of an equation like [tex]\( f^2 = 84 \)[/tex], you need to consider both the positive and the negative square roots. This is because both [tex]\( (f)^2 \)[/tex] and [tex]\( (-f)^2 \)[/tex] equal [tex]\( f^2 \)[/tex].
3. Calculating the Square Root:
- The square root of 84 is approximately 9.165. Therefore, [tex]\( f \)[/tex] could be either positive or negative because squaring either a positive or a negative number gives the same result.
- So, the solutions are:
- [tex]\( f = \sqrt{84} \approx 9.165 \)[/tex]
- [tex]\( f = -\sqrt{84} \approx -9.165 \)[/tex]
4. Conclusion:
- The values of [tex]\( f \)[/tex] that satisfy the equation [tex]\( f^2 = 84 \)[/tex] are approximately [tex]\( 9.165 \)[/tex] and [tex]\( -9.165 \)[/tex].
Therefore, the solution in the context of the fill-in-the-blank question would be:
[tex]\[ f = \pm \sqrt{84} \approx \pm 9.165 \][/tex]
This means that you fill in the blank with [tex]\( \pm 9.165 \)[/tex].
1. Understanding the Equation: The equation [tex]\( f^2 = 84 \)[/tex] tells us that the square of [tex]\( f \)[/tex] equals 84. To find [tex]\( f \)[/tex], we will take the square root of both sides of the equation.
2. Taking the Square Root:
- When you take the square root of both sides of an equation like [tex]\( f^2 = 84 \)[/tex], you need to consider both the positive and the negative square roots. This is because both [tex]\( (f)^2 \)[/tex] and [tex]\( (-f)^2 \)[/tex] equal [tex]\( f^2 \)[/tex].
3. Calculating the Square Root:
- The square root of 84 is approximately 9.165. Therefore, [tex]\( f \)[/tex] could be either positive or negative because squaring either a positive or a negative number gives the same result.
- So, the solutions are:
- [tex]\( f = \sqrt{84} \approx 9.165 \)[/tex]
- [tex]\( f = -\sqrt{84} \approx -9.165 \)[/tex]
4. Conclusion:
- The values of [tex]\( f \)[/tex] that satisfy the equation [tex]\( f^2 = 84 \)[/tex] are approximately [tex]\( 9.165 \)[/tex] and [tex]\( -9.165 \)[/tex].
Therefore, the solution in the context of the fill-in-the-blank question would be:
[tex]\[ f = \pm \sqrt{84} \approx \pm 9.165 \][/tex]
This means that you fill in the blank with [tex]\( \pm 9.165 \)[/tex].
