Solve sqrt{(0-sqrt{5})^2+(-2-2)^2}

$$\sqrt { ( 0 - \sqrt { 5 } ) ^ { 2 } + ( - 2 - 2 ) ^ { 2 } }$$

Evaluate

$$\sqrt{21}\approx 4.582575695$$

Solution Steps

Anything plus zero gives itself.

$$\sqrt{\left(-\sqrt{5}\right)^{2}+\left(-2-2\right)^{2}}$$

Expand \left(-\sqrt{5}\right)^{2}.

$$\sqrt{\left(-1\right)^{2}\left(\sqrt{5}\right)^{2}+\left(-2-2\right)^{2}}$$

Calculate -1 to the power of 2 and get 1.

$$\sqrt{1\left(\sqrt{5}\right)^{2}+\left(-2-2\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{1\times 5+\left(-2-2\right)^{2}}$$

Multiply 1 and 5 to get 5.

$$\sqrt{5+\left(-2-2\right)^{2}}$$

Subtract 2 from -2 to get -4.

$$\sqrt{5+\left(-4\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$\sqrt{5+16}$$

Add 5 and 16 to get 21.

$$\sqrt{21}$$