Solve sqrt{frac{5(1-11)^{2}+(4-11)^2+(11-11)^2+(20-11)^2+(18-11)^2}{5-1}}

$$\sqrt { \frac { 5 ( 1 - 11 ) ^ { 2 } + ( 4 - 11 ) ^ { 2 } + ( 11 - 11 ) ^ { 2 } + ( 20 - 11 ) ^ { 2 } + ( 18 - 11 ) ^ { 2 } } { 5 - 1 } }$$

Evaluate

$$\frac{\sqrt{679}}{2}\approx 13.028814221$$

Solution Steps

Subtract 11 from 1 to get -10.

$$\sqrt{\frac{5\left(-10\right)^{2}+\left(4-11\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calculate -10 to the power of 2 and get 100.

$$\sqrt{\frac{5\times 100+\left(4-11\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Multiply 5 and 100 to get 500.

$$\sqrt{\frac{500+\left(4-11\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Subtract 11 from 4 to get -7.

$$\sqrt{\frac{500+\left(-7\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calculate -7 to the power of 2 and get 49.

$$\sqrt{\frac{500+49+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Add 500 and 49 to get 549.

$$\sqrt{\frac{549+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Subtract 11 from 11 to get 0.

$$\sqrt{\frac{549+0^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calculate 0 to the power of 2 and get 0.

$$\sqrt{\frac{549+0+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Add 549 and 0 to get 549.

$$\sqrt{\frac{549+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Subtract 11 from 20 to get 9.

$$\sqrt{\frac{549+9^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{\frac{549+81+\left(18-11\right)^{2}}{5-1}}$$

Add 549 and 81 to get 630.

$$\sqrt{\frac{630+\left(18-11\right)^{2}}{5-1}}$$

Subtract 11 from 18 to get 7.

$$\sqrt{\frac{630+7^{2}}{5-1}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{\frac{630+49}{5-1}}$$

Add 630 and 49 to get 679.

$$\sqrt{\frac{679}{5-1}}$$

Subtract 1 from 5 to get 4.

$$\sqrt{\frac{679}{4}}$$

Rewrite the square root of the division \sqrt{\frac{679}{4}} as the division of square roots \frac{\sqrt{679}}{\sqrt{4}}.

$$\frac{\sqrt{679}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{679}}{2}$$