Solve 1^2+2^2+4^2+5^2+{7}^{2}+{8}^{2}+{10}^{2}+{11}^2+{13}^2+{14}^2+{16}^2

$${ 1 }^{ 2 } + { 2 }^{ 2 } + { 4 }^{ 2 } + { 5 }^{ 2 } + { 7 }^{ 2 } + { 8 }^{ 2 } + { 10 }^{ 2 } + { 11 }^{ 2 } + { 13 }^{ 2 } + { 14 }^{ 2 } + { 16 }^{ 2 }$$

Evaluate

$$1001$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$1+2^{2}+4^{2}+5^{2}+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1+4+4^{2}+5^{2}+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Add 1 and 4 to get 5.

$$5+4^{2}+5^{2}+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 4 to the power of 2 and get 16.

$$5+16+5^{2}+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Add 5 and 16 to get 21.

$$21+5^{2}+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 5 to the power of 2 and get 25.

$$21+25+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Add 21 and 25 to get 46.

$$46+7^{2}+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 7 to the power of 2 and get 49.

$$46+49+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Add 46 and 49 to get 95.

$$95+8^{2}+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 8 to the power of 2 and get 64.

$$95+64+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Add 95 and 64 to get 159.

$$159+10^{2}+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 10 to the power of 2 and get 100.

$$159+100+11^{2}+13^{2}+14^{2}+16^{2}$$

Add 159 and 100 to get 259.

$$259+11^{2}+13^{2}+14^{2}+16^{2}$$

Calculate 11 to the power of 2 and get 121.

$$259+121+13^{2}+14^{2}+16^{2}$$

Add 259 and 121 to get 380.

$$380+13^{2}+14^{2}+16^{2}$$

Calculate 13 to the power of 2 and get 169.

$$380+169+14^{2}+16^{2}$$

Add 380 and 169 to get 549.

$$549+14^{2}+16^{2}$$

Calculate 14 to the power of 2 and get 196.

$$549+196+16^{2}$$

Add 549 and 196 to get 745.

$$745+16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$745+256$$

Add 745 and 256 to get 1001.

$$1001$$

Factor

$$7\times 11\times 13$$