Solve sqrt{159+27-17}+sqrt{21^2+28^2}-sqrt{15^2+16^2+3}-sqrt{30+6}

$$\sqrt { 159 + 27 - 17 } + \sqrt { 21 ^ { 2 } + 28 ^ { 2 } } - \sqrt { 15 ^ { 2 } + 16 ^ { 2 } + 3 } - \sqrt { 30 + 6 }$$

Evaluate

$$20$$

Solution Steps

Add 159 and 27 to get 186.

$$\sqrt{186-17}+\sqrt{21^{2}+28^{2}}-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Subtract 17 from 186 to get 169.

$$\sqrt{169}+\sqrt{21^{2}+28^{2}}-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Calculate the square root of 169 and get 13.

$$13+\sqrt{21^{2}+28^{2}}-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Calculate 21 to the power of 2 and get 441.

$$13+\sqrt{441+28^{2}}-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Calculate 28 to the power of 2 and get 784.

$$13+\sqrt{441+784}-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Add 441 and 784 to get 1225.

$$13+\sqrt{1225}-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Calculate the square root of 1225 and get 35.

$$13+35-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Add 13 and 35 to get 48.

$$48-\sqrt{15^{2}+16^{2}+3}-\sqrt{30+6}$$

Calculate 15 to the power of 2 and get 225.

$$48-\sqrt{225+16^{2}+3}-\sqrt{30+6}$$

Calculate 16 to the power of 2 and get 256.

$$48-\sqrt{225+256+3}-\sqrt{30+6}$$

Add 225 and 256 to get 481.

$$48-\sqrt{481+3}-\sqrt{30+6}$$

Add 481 and 3 to get 484.

$$48-\sqrt{484}-\sqrt{30+6}$$

Calculate the square root of 484 and get 22.

$$48-22-\sqrt{30+6}$$

Subtract 22 from 48 to get 26.

$$26-\sqrt{30+6}$$

Add 30 and 6 to get 36.

$$26-\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$26-6$$

Subtract 6 from 26 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$