Solve sqrt{left(13.3-7right)^2+left(26.6-7right)^2+left(5-7right)^2+left(7-7right)^2/7}

$$\sqrt{ \frac{ { \left(13.3-7 \right) }^{ 2 } + { \left(26.6-7 \right) }^{ 2 } + { \left(5-7 \right) }^{ 2 } + { \left(7-7 \right) }^{ 2 } }{ 7 } }$$

Evaluate

$$\frac{\sqrt{299495}}{70}\approx 7.818019479$$

Solution Steps

Subtract 7 from 13.3 to get 6.3.

$$\sqrt{\frac{6.3^{2}+\left(26.6-7\right)^{2}+\left(5-7\right)^{2}+\left(7-7\right)^{2}}{7}}$$

Calculate 6.3 to the power of 2 and get 39.69.

$$\sqrt{\frac{39.69+\left(26.6-7\right)^{2}+\left(5-7\right)^{2}+\left(7-7\right)^{2}}{7}}$$

Subtract 7 from 26.6 to get 19.6.

$$\sqrt{\frac{39.69+19.6^{2}+\left(5-7\right)^{2}+\left(7-7\right)^{2}}{7}}$$

Calculate 19.6 to the power of 2 and get 384.16.

$$\sqrt{\frac{39.69+384.16+\left(5-7\right)^{2}+\left(7-7\right)^{2}}{7}}$$

Add 39.69 and 384.16 to get 423.85.

$$\sqrt{\frac{423.85+\left(5-7\right)^{2}+\left(7-7\right)^{2}}{7}}$$

Subtract 7 from 5 to get -2.

$$\sqrt{\frac{423.85+\left(-2\right)^{2}+\left(7-7\right)^{2}}{7}}$$

Calculate -2 to the power of 2 and get 4.

$$\sqrt{\frac{423.85+4+\left(7-7\right)^{2}}{7}}$$

Add 423.85 and 4 to get 427.85.

$$\sqrt{\frac{427.85+\left(7-7\right)^{2}}{7}}$$

Subtract 7 from 7 to get 0.

$$\sqrt{\frac{427.85+0^{2}}{7}}$$

Calculate 0 to the power of 2 and get 0.

$$\sqrt{\frac{427.85+0}{7}}$$

Add 427.85 and 0 to get 427.85.

$$\sqrt{\frac{427.85}{7}}$$

Expand \frac{427.85}{7} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{42785}{700}}$$

Reduce the fraction \frac{42785}{700} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{8557}{140}}$$

Rewrite the square root of the division \sqrt{\frac{8557}{140}} as the division of square roots \frac{\sqrt{8557}}{\sqrt{140}}.

$$\frac{\sqrt{8557}}{\sqrt{140}}$$

Factor 140=2^{2}\times 35. Rewrite the square root of the product \sqrt{2^{2}\times 35} as the product of square roots \sqrt{2^{2}}\sqrt{35}. Take the square root of 2^{2}.

$$\frac{\sqrt{8557}}{2\sqrt{35}}$$

Rationalize the denominator of \frac{\sqrt{8557}}{2\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$\frac{\sqrt{8557}\sqrt{35}}{2\left(\sqrt{35}\right)^{2}}$$

The square of \sqrt{35} is 35.

$$\frac{\sqrt{8557}\sqrt{35}}{2\times 35}$$

To multiply \sqrt{8557} and \sqrt{35}, multiply the numbers under the square root.

$$\frac{\sqrt{299495}}{2\times 35}$$

Multiply 2 and 35 to get 70.

$$\frac{\sqrt{299495}}{70}$$