Solve sqrt{(3+1/2-0)^2+(3+0/2-1)^2+(3-0)^2}

$$\sqrt { ( \frac { 3 + 1 } { 2 } - 0 ) ^ { 2 } + ( \frac { 3 + 0 } { 2 } - 1 ) ^ { 2 } + ( 3 - 0 ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{53}}{2}\approx 3.640054945$$

Solution Steps

Add 3 and 1 to get 4.

$$\sqrt{\left(\frac{4}{2}-0\right)^{2}+\left(\frac{3+0}{2}-1\right)^{2}+\left(3-0\right)^{2}}$$

Divide 4 by 2 to get 2.

$$\sqrt{\left(2-0\right)^{2}+\left(\frac{3+0}{2}-1\right)^{2}+\left(3-0\right)^{2}}$$

Subtract 0 from 2 to get 2.

$$\sqrt{2^{2}+\left(\frac{3+0}{2}-1\right)^{2}+\left(3-0\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+\left(\frac{3+0}{2}-1\right)^{2}+\left(3-0\right)^{2}}$$

Add 3 and 0 to get 3.

$$\sqrt{4+\left(\frac{3}{2}-1\right)^{2}+\left(3-0\right)^{2}}$$

Subtract 1 from \frac{3}{2} to get \frac{1}{2}.

$$\sqrt{4+\left(\frac{1}{2}\right)^{2}+\left(3-0\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\sqrt{4+\frac{1}{4}+\left(3-0\right)^{2}}$$

Add 4 and \frac{1}{4} to get \frac{17}{4}.

$$\sqrt{\frac{17}{4}+\left(3-0\right)^{2}}$$

Subtract 0 from 3 to get 3.

$$\sqrt{\frac{17}{4}+3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{\frac{17}{4}+9}$$

Add \frac{17}{4} and 9 to get \frac{53}{4}.

$$\sqrt{\frac{53}{4}}$$

Rewrite the square root of the division \sqrt{\frac{53}{4}} as the division of square roots \frac{\sqrt{53}}{\sqrt{4}}.

$$\frac{\sqrt{53}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{53}}{2}$$