Solve 3.33^2+3.33^2+2.33^2+1.33^2+{0.33}^{2}+{0.33}^{2}+{0.67}^{2}+{1.67}^2+{2.67}^2+{2.67}^2+{3.67}^2

$${ 3.33 }^{ 2 } + { 3.33 }^{ 2 } + { 2.33 }^{ 2 } + { 1.33 }^{ 2 } + { 0.33 }^{ 2 } + { 0.33 }^{ 2 } + { 0.67 }^{ 2 } + { 1.67 }^{ 2 } + { 2.67 }^{ 2 } + { 2.67 }^{ 2 } + { 3.67 }^{ 2 }$$

Evaluate

$$60.5579$$

Solution Steps

Calculate 3.33 to the power of 2 and get 11.0889.

$$11.0889+3.33^{2}+2.33^{2}+1.33^{2}+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 3.33 to the power of 2 and get 11.0889.

$$11.0889+11.0889+2.33^{2}+1.33^{2}+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 11.0889 and 11.0889 to get 22.1778.

$$22.1778+2.33^{2}+1.33^{2}+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 2.33 to the power of 2 and get 5.4289.

$$22.1778+5.4289+1.33^{2}+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 22.1778 and 5.4289 to get 27.6067.

$$27.6067+1.33^{2}+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 1.33 to the power of 2 and get 1.7689.

$$27.6067+1.7689+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 27.6067 and 1.7689 to get 29.3756.

$$29.3756+0.33^{2}+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 0.33 to the power of 2 and get 0.1089.

$$29.3756+0.1089+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 29.3756 and 0.1089 to get 29.4845.

$$29.4845+0.33^{2}+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 0.33 to the power of 2 and get 0.1089.

$$29.4845+0.1089+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 29.4845 and 0.1089 to get 29.5934.

$$29.5934+0.67^{2}+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 0.67 to the power of 2 and get 0.4489.

$$29.5934+0.4489+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 29.5934 and 0.4489 to get 30.0423.

$$30.0423+1.67^{2}+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 1.67 to the power of 2 and get 2.7889.

$$30.0423+2.7889+2.67^{2}+2.67^{2}+3.67^{2}$$

Add 30.0423 and 2.7889 to get 32.8312.

$$32.8312+2.67^{2}+2.67^{2}+3.67^{2}$$

Calculate 2.67 to the power of 2 and get 7.1289.

$$32.8312+7.1289+2.67^{2}+3.67^{2}$$

Add 32.8312 and 7.1289 to get 39.9601.

$$39.9601+2.67^{2}+3.67^{2}$$

Calculate 2.67 to the power of 2 and get 7.1289.

$$39.9601+7.1289+3.67^{2}$$

Add 39.9601 and 7.1289 to get 47.089.

$$47.089+3.67^{2}$$

Calculate 3.67 to the power of 2 and get 13.4689.

$$47.089+13.4689$$

Add 47.089 and 13.4689 to get 60.5579.

$$60.5579$$

Factor

$$\frac{13 \cdot 37 \cdot 1259}{2 ^ {4} \cdot 5 ^ {4}} = 60\frac{5579}{10000} = 60.5579$$