Solve sqrt{9^2+(2sqrt{2})^2}

$$\sqrt { 9 ^ { 2 } + ( 2 \sqrt { 2 } ) ^ { 2 } }$$

Evaluate

$$\sqrt{89}\approx 9.433981132$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\sqrt{81+\left(2\sqrt{2}\right)^{2}}$$

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

$$\sqrt{81+2^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{81+4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{81+4\times 2}$$

Multiply 4 and 2 to get 8.

$$\sqrt{81+8}$$

Add 81 and 8 to get 89.

$$\sqrt{89}$$