Solve 168=v^2

$$168 = v ^ { 2 }$$

Solve for v

$$v=2\sqrt{42}\approx 12.961481397$$

$$v=-2\sqrt{42}\approx -12.961481397$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$v^{2}=168$$

Take the square root of both sides of the equation.

$$v=2\sqrt{42} v=-2\sqrt{42}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$v^{2}=168$$

Subtract 168 from both sides.

$$v^{2}-168=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -168 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-168\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-168\right)}}{2}$$

Multiply -4 times -168.

$$v=\frac{0±\sqrt{672}}{2}$$

Take the square root of 672.

$$v=\frac{0±4\sqrt{42}}{2}$$

Now solve the equation v=\frac{0±4\sqrt{42}}{2} when ± is plus.

$$v=2\sqrt{42}$$

Now solve the equation v=\frac{0±4\sqrt{42}}{2} when ± is minus.

$$v=-2\sqrt{42}$$

The equation is now solved.

$$v=2\sqrt{42} v=-2\sqrt{42}$$