Solve 1^2+2^2+3^2+4^2+{5}^{2}+{6}^{2}+{7}^2+{8}^2+{9}^2+{10}^2=

$${ 1 }^{ 2 } + { 2 }^{ 2 } + { 3 }^{ 2 } + { 4 }^{ 2 } + { 5 }^{ 2 } + { 6 }^{ 2 } + { 7 }^{ 2 } + { 8 }^{ 2 } + { 9 }^{ 2 } + { 10 }^{ 2 } =$$

Evaluate

$$385$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$1+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1+4+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Add 1 and 4 to get 5.

$$5+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Calculate 3 to the power of 2 and get 9.

$$5+9+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Add 5 and 9 to get 14.

$$14+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Calculate 4 to the power of 2 and get 16.

$$14+16+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Add 14 and 16 to get 30.

$$30+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Calculate 5 to the power of 2 and get 25.

$$30+25+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Add 30 and 25 to get 55.

$$55+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}$$

Calculate 6 to the power of 2 and get 36.

$$55+36+7^{2}+8^{2}+9^{2}+10^{2}$$

Add 55 and 36 to get 91.

$$91+7^{2}+8^{2}+9^{2}+10^{2}$$

Calculate 7 to the power of 2 and get 49.

$$91+49+8^{2}+9^{2}+10^{2}$$

Add 91 and 49 to get 140.

$$140+8^{2}+9^{2}+10^{2}$$

Calculate 8 to the power of 2 and get 64.

$$140+64+9^{2}+10^{2}$$

Add 140 and 64 to get 204.

$$204+9^{2}+10^{2}$$

Calculate 9 to the power of 2 and get 81.

$$204+81+10^{2}$$

Add 204 and 81 to get 285.

$$285+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$285+100$$

Add 285 and 100 to get 385.

$$385$$

Factor

$$5\times 7\times 11$$