Solve sqrt{left(20-4right)^2}+left(16-4right)^2+left(8-4right)^2+left(4-4right)^2

$$\sqrt{ { \left(20-4 \right) }^{ 2 } } + { \left(16-4 \right) }^{ 2 } + { \left(8-4 \right) }^{ 2 } + { \left(4-4 \right) }^{ 2 }$$

Evaluate

$$176$$

Solution Steps

Subtract 4 from 20 to get 16.

$$\sqrt{16^{2}}+\left(16-4\right)^{2}+\left(8-4\right)^{2}+\left(4-4\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$\sqrt{256}+\left(16-4\right)^{2}+\left(8-4\right)^{2}+\left(4-4\right)^{2}$$

Calculate the square root of 256 and get 16.

$$16+\left(16-4\right)^{2}+\left(8-4\right)^{2}+\left(4-4\right)^{2}$$

Subtract 4 from 16 to get 12.

$$16+12^{2}+\left(8-4\right)^{2}+\left(4-4\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$16+144+\left(8-4\right)^{2}+\left(4-4\right)^{2}$$

Add 16 and 144 to get 160.

$$160+\left(8-4\right)^{2}+\left(4-4\right)^{2}$$

Subtract 4 from 8 to get 4.

$$160+4^{2}+\left(4-4\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$160+16+\left(4-4\right)^{2}$$

Add 160 and 16 to get 176.

$$176+\left(4-4\right)^{2}$$

Subtract 4 from 4 to get 0.

$$176+0^{2}$$

Calculate 0 to the power of 2 and get 0.

$$176+0$$

Add 176 and 0 to get 176.

$$176$$

Factor

$$2^{4}\times 11$$