v^2=7
You asked:
Solve the equation \({v}^{2} = 7\) for the variable \(v\).
MathBot Answer:
\[\begin{aligned}v &= \sqrt{7} \approx 2.6457513\\v &= - \sqrt{7} \approx -2.6457513\end{aligned}\]
Take the square root of both sides of the equation $$\begin{aligned}v^{2} &= 7 \\ \sqrt{v^{2}} &= \sqrt{7} \end{aligned}$$
Remember that both positive and negative numbers will result in a positive number when squared, so a square root will have both a positive and a negative answer. $$\begin{aligned}v &= \pm \sqrt{7} \\ v = \sqrt{7} &,\, v=-\sqrt{7}\end{aligned}$$