Solve sqrt{left(1-(-1)right)^2+left(3-1right)^2+left(2-4right)^2}

$$\sqrt{ { \left(1-(-1) \right) }^{ 2 } + { \left(3-1 \right) }^{ 2 } + { \left(2-4 \right) }^{ 2 } }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

The opposite of -1 is 1.

$$\sqrt{\left(1+1\right)^{2}+\left(3-1\right)^{2}+\left(2-4\right)^{2}}$$

Add 1 and 1 to get 2.

$$\sqrt{2^{2}+\left(3-1\right)^{2}+\left(2-4\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+\left(3-1\right)^{2}+\left(2-4\right)^{2}}$$

Subtract 1 from 3 to get 2.

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

Calculate 2 to the power of 2 and get 4.

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

Add 4 and 4 to get 8.

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

Subtract 4 from 2 to get -2.

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

Calculate -2 to the power of 2 and get 4.

$$\sqrt{8+4}$$

Add 8 and 4 to get 12.

$$\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}$$