Solve sqrt{frac{28.6^2+40.6^2+50.4^2+3.6^2+{22.4}^2}{20}}

$$\sqrt{ \frac{ { 28.6 }^{ 2 } + { 40.6 }^{ 2 } + { 50.4 }^{ 2 } + { 3.6 }^{ 2 } + { 22.4 }^{ 2 } }{ 20 } }$$

Evaluate

$$\frac{\sqrt{27606}}{10}\approx 16.615053416$$

Solution Steps

Calculate 28.6 to the power of 2 and get 817.96.

$$\sqrt{\frac{817.96+40.6^{2}+50.4^{2}+3.6^{2}+22.4^{2}}{20}}$$

Calculate 40.6 to the power of 2 and get 1648.36.

$$\sqrt{\frac{817.96+1648.36+50.4^{2}+3.6^{2}+22.4^{2}}{20}}$$

Add 817.96 and 1648.36 to get 2466.32.

$$\sqrt{\frac{2466.32+50.4^{2}+3.6^{2}+22.4^{2}}{20}}$$

Calculate 50.4 to the power of 2 and get 2540.16.

$$\sqrt{\frac{2466.32+2540.16+3.6^{2}+22.4^{2}}{20}}$$

Add 2466.32 and 2540.16 to get 5006.48.

$$\sqrt{\frac{5006.48+3.6^{2}+22.4^{2}}{20}}$$

Calculate 3.6 to the power of 2 and get 12.96.

$$\sqrt{\frac{5006.48+12.96+22.4^{2}}{20}}$$

Add 5006.48 and 12.96 to get 5019.44.

$$\sqrt{\frac{5019.44+22.4^{2}}{20}}$$

Calculate 22.4 to the power of 2 and get 501.76.

$$\sqrt{\frac{5019.44+501.76}{20}}$$

Add 5019.44 and 501.76 to get 5521.2.

$$\sqrt{\frac{5521.2}{20}}$$

Expand \frac{5521.2}{20} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{55212}{200}}$$

Reduce the fraction \frac{55212}{200} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{13803}{50}}$$

Rewrite the square root of the division \sqrt{\frac{13803}{50}} as the division of square roots \frac{\sqrt{13803}}{\sqrt{50}}.

$$\frac{\sqrt{13803}}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{\sqrt{13803}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{13803}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{13803}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{13803}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{13803} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{27606}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{\sqrt{27606}}{10}$$