Solve sigma^2=88^2/12-7.33^2

$$\sigma ^ { 2 } = \frac { 88 ^ { 2 } } { 12 } - 7.33 ^ { 2 }$$

Solve for σ

$$\sigma =\frac{\sqrt{53244399}}{300}\approx 24.322919918$$

$$\sigma =-\frac{\sqrt{53244399}}{300}\approx -24.322919918$$

Steps by Finding Square Root

Multiply both sides of the equation by 12.

$$12\sigma ^{2}=88^{2}-12\times 7.33^{2}$$

Calculate 88 to the power of 2 and get 7744.

$$12\sigma ^{2}=7744-12\times 7.33^{2}$$

Calculate 7.33 to the power of 2 and get 53.7289.

$$12\sigma ^{2}=7744-12\times 53.7289$$

Multiply 12 and 53.7289 to get 644.7468.

$$12\sigma ^{2}=7744-644.7468$$

Subtract 644.7468 from 7744 to get 7099.2532.

$$12\sigma ^{2}=7099.2532$$

Divide both sides by 12.

$$\sigma ^{2}=\frac{7099.2532}{12}$$

Expand \frac{7099.2532}{12} by multiplying both numerator and the denominator by 10000.

$$\sigma ^{2}=\frac{70992532}{120000}$$

Reduce the fraction \frac{70992532}{120000} to lowest terms by extracting and canceling out 4.

$$\sigma ^{2}=\frac{17748133}{30000}$$

Take the square root of both sides of the equation.

$$\sigma =\frac{\sqrt{53244399}}{300} \sigma =-\frac{\sqrt{53244399}}{300}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 12.

$$12\sigma ^{2}=88^{2}-12\times 7.33^{2}$$

Calculate 88 to the power of 2 and get 7744.

$$12\sigma ^{2}=7744-12\times 7.33^{2}$$

Calculate 7.33 to the power of 2 and get 53.7289.

$$12\sigma ^{2}=7744-12\times 53.7289$$

Multiply 12 and 53.7289 to get 644.7468.

$$12\sigma ^{2}=7744-644.7468$$

Subtract 644.7468 from 7744 to get 7099.2532.

$$12\sigma ^{2}=7099.2532$$

Subtract 7099.2532 from both sides.

$$12\sigma ^{2}-7099.2532=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -7099.2532 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\sigma =\frac{0±\sqrt{0^{2}-4\times 12\left(-7099.2532\right)}}{2\times 12}$$

Square 0.

$$\sigma =\frac{0±\sqrt{-4\times 12\left(-7099.2532\right)}}{2\times 12}$$

Multiply -4 times 12.

$$\sigma =\frac{0±\sqrt{-48\left(-7099.2532\right)}}{2\times 12}$$

Multiply -48 times -7099.2532.

$$\sigma =\frac{0±\sqrt{340764.1536}}{2\times 12}$$

Take the square root of 340764.1536.

$$\sigma =\frac{0±\frac{2\sqrt{53244399}}{25}}{2\times 12}$$

Multiply 2 times 12.

$$\sigma =\frac{0±\frac{2\sqrt{53244399}}{25}}{24}$$

Now solve the equation \sigma =\frac{0±\frac{2\sqrt{53244399}}{25}}{24} when ± is plus.

$$\sigma =\frac{\sqrt{53244399}}{300}$$

Now solve the equation \sigma =\frac{0±\frac{2\sqrt{53244399}}{25}}{24} when ± is minus.

$$\sigma =-\frac{\sqrt{53244399}}{300}$$

The equation is now solved.

$$\sigma =\frac{\sqrt{53244399}}{300} \sigma =-\frac{\sqrt{53244399}}{300}$$