Solve 22/7*gamma^2=4

$$\frac { 22 } { 7 } \times \gamma ^ { 2 } = 4$$

Solve for γ

$$\gamma =\frac{\sqrt{154}}{11}\approx 1.12815215$$

$$\gamma =-\frac{\sqrt{154}}{11}\approx -1.12815215$$

Steps by Finding Square Root

Multiply both sides by \frac{7}{22}, the reciprocal of \frac{22}{7}.

$$\gamma ^{2}=4\times \frac{7}{22}$$

Multiply 4 and \frac{7}{22} to get \frac{14}{11}.

$$\gamma ^{2}=\frac{14}{11}$$

Take the square root of both sides of the equation.

$$\gamma =\frac{\sqrt{154}}{11} \gamma =-\frac{\sqrt{154}}{11}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{7}{22}, the reciprocal of \frac{22}{7}.

$$\gamma ^{2}=4\times \frac{7}{22}$$

Multiply 4 and \frac{7}{22} to get \frac{14}{11}.

$$\gamma ^{2}=\frac{14}{11}$$

Subtract \frac{14}{11} from both sides.

$$\gamma ^{2}-\frac{14}{11}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{14}{11} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\gamma =\frac{0±\sqrt{0^{2}-4\left(-\frac{14}{11}\right)}}{2}$$

Square 0.

$$\gamma =\frac{0±\sqrt{-4\left(-\frac{14}{11}\right)}}{2}$$

Multiply -4 times -\frac{14}{11}.

$$\gamma =\frac{0±\sqrt{\frac{56}{11}}}{2}$$

Take the square root of \frac{56}{11}.

$$\gamma =\frac{0±\frac{2\sqrt{154}}{11}}{2}$$

Now solve the equation \gamma =\frac{0±\frac{2\sqrt{154}}{11}}{2} when ± is plus.

$$\gamma =\frac{\sqrt{154}}{11}$$

Now solve the equation \gamma =\frac{0±\frac{2\sqrt{154}}{11}}{2} when ± is minus.

$$\gamma =-\frac{\sqrt{154}}{11}$$

The equation is now solved.

$$\gamma =\frac{\sqrt{154}}{11} \gamma =-\frac{\sqrt{154}}{11}$$