Answer :
To solve the equation [tex]\( f^2 = 84 \)[/tex], we are looking for the value or values of [tex]\( f \)[/tex] that satisfy this equation. To find the solution, follow these steps:
1. Understand the Equation: The equation [tex]\( f^2 = 84 \)[/tex] means that we need to find a number [tex]\( f \)[/tex] which, when squared, results in 84.
2. Solving for [tex]\( f \)[/tex]: We can find [tex]\( f \)[/tex] by taking the square root of both sides of the equation. This gives us:
[tex]\[
f = \sqrt{84}
\][/tex]
and also considering the negative root:
[tex]\[
f = -\sqrt{84}
\][/tex]
3. Calculate the Square Roots: When you calculate the square root of 84, you will find two possible values for [tex]\( f \)[/tex]. The positive root is approximately 9.16515138991168, and the negative root is approximately -9.16515138991168.
4. Conclusion: The complete set of solutions for [tex]\( f \)[/tex] are:
[tex]\[
f \approx 9.16515138991168 \quad \text{or} \quad f \approx -9.16515138991168
\][/tex]
These are the possible values of [tex]\( f \)[/tex] that satisfy the original equation [tex]\( f^2 = 84 \)[/tex].
1. Understand the Equation: The equation [tex]\( f^2 = 84 \)[/tex] means that we need to find a number [tex]\( f \)[/tex] which, when squared, results in 84.
2. Solving for [tex]\( f \)[/tex]: We can find [tex]\( f \)[/tex] by taking the square root of both sides of the equation. This gives us:
[tex]\[
f = \sqrt{84}
\][/tex]
and also considering the negative root:
[tex]\[
f = -\sqrt{84}
\][/tex]
3. Calculate the Square Roots: When you calculate the square root of 84, you will find two possible values for [tex]\( f \)[/tex]. The positive root is approximately 9.16515138991168, and the negative root is approximately -9.16515138991168.
4. Conclusion: The complete set of solutions for [tex]\( f \)[/tex] are:
[tex]\[
f \approx 9.16515138991168 \quad \text{or} \quad f \approx -9.16515138991168
\][/tex]
These are the possible values of [tex]\( f \)[/tex] that satisfy the original equation [tex]\( f^2 = 84 \)[/tex].
