Question

Solve the equation. $\sqrt{\frac{1000}{10}}=n^2-54$ .

Answer 1

Solve the given equation.

$$\begin{gathered} \sqrt{\frac{1000}{10}}=n^2-54 \\ \Rightarrow \sqrt{100}=n^2-54\mathbf{}\mathbf{} \\ \Rightarrow 10=n^2-54(\mathrm{Evaluate}\mathrm{the}\mathrm{square}\mathrm{root}) \\ \Rightarrow n^2=64(\mathrm{Add}54\mathrm{each}\mathrm{side}) \\ \Rightarrow n=\pm \sqrt{64}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}(\mathrm{Take}\mathrm{the}\mathrm{square}\mathrm{root}\mathrm{of}\mathrm{each}\mathrm{side}) \\ \Rightarrow n=\pm 8\mathbf{}\mathbf{}\mathbf{}\mathbf{} \end{gathered}$$

Hence, the solutions are $n=+8$and $n=-8$.