Solve sqrt{51+2^{2}+3^{2}}-sqrt{3^{2}+4^2}+sqrt{6^2+3^3+1^4}

$$\sqrt { 51 + 2 ^ { 2 } + 3 ^ { 2 } } - \sqrt { 3 ^ { 2 } + 4 ^ { 2 } } + \sqrt { 6 ^ { 2 } + 3 ^ { 3 } + 1 ^ { 4 } }$$

Evaluate

$$11$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\sqrt{51+4+3^{2}}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Add 51 and 4 to get 55.

$$\sqrt{55+3^{2}}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{55+9}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Add 55 and 9 to get 64.

$$\sqrt{64}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Calculate the square root of 64 and get 8.

$$8-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$8-\sqrt{9+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$8-\sqrt{9+16}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Add 9 and 16 to get 25.

$$8-\sqrt{25}+\sqrt{6^{2}+3^{3}+1^{4}}$$

Calculate the square root of 25 and get 5.

$$8-5+\sqrt{6^{2}+3^{3}+1^{4}}$$

Subtract 5 from 8 to get 3.

$$3+\sqrt{6^{2}+3^{3}+1^{4}}$$

Calculate 6 to the power of 2 and get 36.

$$3+\sqrt{36+3^{3}+1^{4}}$$

Calculate 3 to the power of 3 and get 27.

$$3+\sqrt{36+27+1^{4}}$$

Add 36 and 27 to get 63.

$$3+\sqrt{63+1^{4}}$$

Calculate 1 to the power of 4 and get 1.

$$3+\sqrt{63+1}$$

Add 63 and 1 to get 64.

$$3+\sqrt{64}$$

Calculate the square root of 64 and get 8.

$$3+8$$

Add 3 and 8 to get 11.

$$11$$

Factor

$$11$$