Solve sqrt{(0+2sqrt{2})^2+(sqrt{3}+0)^2}

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

Evaluate

$$\sqrt{11}\approx 3.31662479$$

Solution Steps

Anything plus zero gives itself.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{2} is 2.

$$\sqrt{4\times 2+\left(\sqrt{3}+0\right)^{2}}$$

Multiply 4 and 2 to get 8.

$$\sqrt{8+\left(\sqrt{3}+0\right)^{2}}$$

Anything plus zero gives itself.

$$\sqrt{8+\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{8+3}$$

Add 8 and 3 to get 11.

$$\sqrt{11}$$