1. The problem is to solve for $f$ given the equation $f^2 = 84$. 2. The formula used is the square root property: if $x^2 = a$, then $x = \pm\sqrt{a}$. 3. Applying this to the problem, we take the square root of both sides: $$f = \pm\sqrt{84}$$ 4. Simplify $\sqrt{84}$ by factoring: $$\sqrt{84} = \sqrt{4 \times 21} = \sqrt{4} \times \sqrt{21} = 2\sqrt{21}$$ 5. Therefore, the solutions are: $$f = \pm 2\sqrt{21}$$ 6. This means $f$ can be either $2\sqrt{21}$ or $-2\sqrt{21}$. 7. In plain language, when you square a number and get 84, the original number could be positive or negative $2\sqrt{21}$ because squaring either gives 84.