Solve sqrt{11^2+13^2+110}+sqrt{18^2+8^2+{3}^2+3+3+sqrt{9}}

$$\sqrt{ { 11 }^{ 2 } + { 13 }^{ 2 } +110 } + \sqrt{ { 18 }^{ 2 } + { 8 }^{ 2 } + { 3 }^{ 2 } +3+3+ \sqrt{ 9 } }$$

Evaluate

$$\sqrt{406}+20\approx 40.14944168$$

Solution Steps

Calculate 11 to the power of 2 and get 121.

$$\sqrt{121+13^{2}+110}+\sqrt{18^{2}+8^{2}+3^{2}+3+3+\sqrt{9}}$$

Calculate 13 to the power of 2 and get 169.

$$\sqrt{121+169+110}+\sqrt{18^{2}+8^{2}+3^{2}+3+3+\sqrt{9}}$$

Add 121 and 169 to get 290.

$$\sqrt{290+110}+\sqrt{18^{2}+8^{2}+3^{2}+3+3+\sqrt{9}}$$

Add 290 and 110 to get 400.

$$\sqrt{400}+\sqrt{18^{2}+8^{2}+3^{2}+3+3+\sqrt{9}}$$

Calculate the square root of 400 and get 20.

$$20+\sqrt{18^{2}+8^{2}+3^{2}+3+3+\sqrt{9}}$$

Calculate 18 to the power of 2 and get 324.

$$20+\sqrt{324+8^{2}+3^{2}+3+3+\sqrt{9}}$$

Calculate 8 to the power of 2 and get 64.

$$20+\sqrt{324+64+3^{2}+3+3+\sqrt{9}}$$

Add 324 and 64 to get 388.

$$20+\sqrt{388+3^{2}+3+3+\sqrt{9}}$$

Calculate 3 to the power of 2 and get 9.

$$20+\sqrt{388+9+3+3+\sqrt{9}}$$

Add 388 and 9 to get 397.

$$20+\sqrt{397+3+3+\sqrt{9}}$$

Add 397 and 3 to get 400.

$$20+\sqrt{400+3+\sqrt{9}}$$

Add 400 and 3 to get 403.

$$20+\sqrt{403+\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$20+\sqrt{403+3}$$

Add 403 and 3 to get 406.

$$20+\sqrt{406}$$