Solve (22^2+25^2+30^2+30^2+{37}^2+{60}^2-6*{34}^2)div{6}^2

$$( { 22 }^{ 2 } + { 25 }^{ 2 } + { 30 }^{ 2 } + { 30 }^{ 2 } + { 37 }^{ 2 } + { 60 }^{ 2 } -6 \times { 34 }^{ 2 } ) \div { 6 }^{ 2 }$$

Evaluate

$$\frac{157}{6}\approx 26.166666667$$

Solution Steps

Calculate 22 to the power of 2 and get 484.

$$\frac{484+25^{2}+30^{2}+30^{2}+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{484+625+30^{2}+30^{2}+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Add 484 and 625 to get 1109.

$$\frac{1109+30^{2}+30^{2}+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{1109+900+30^{2}+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Add 1109 and 900 to get 2009.

$$\frac{2009+30^{2}+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{2009+900+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Add 2009 and 900 to get 2909.

$$\frac{2909+37^{2}+60^{2}-6\times 34^{2}}{6^{2}}$$

Calculate 37 to the power of 2 and get 1369.

$$\frac{2909+1369+60^{2}-6\times 34^{2}}{6^{2}}$$

Add 2909 and 1369 to get 4278.

$$\frac{4278+60^{2}-6\times 34^{2}}{6^{2}}$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{4278+3600-6\times 34^{2}}{6^{2}}$$

Add 4278 and 3600 to get 7878.

$$\frac{7878-6\times 34^{2}}{6^{2}}$$

Calculate 34 to the power of 2 and get 1156.

$$\frac{7878-6\times 1156}{6^{2}}$$

Multiply 6 and 1156 to get 6936.

$$\frac{7878-6936}{6^{2}}$$

Subtract 6936 from 7878 to get 942.

$$\frac{942}{6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{942}{36}$$

Reduce the fraction \frac{942}{36} to lowest terms by extracting and canceling out 6.

$$\frac{157}{6}$$

Factor

$$\frac{157}{2 \cdot 3} = 26\frac{1}{6} = 26.166666666666668$$