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

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

Evaluate

$$\sqrt{26}\approx 5.099019514$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

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

Expand \left(3\sqrt{2}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$\sqrt{8+9\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{8+9\times 2}$$

Multiply 9 and 2 to get 18.

$$\sqrt{8+18}$$

Add 8 and 18 to get 26.

$$\sqrt{26}$$