Solve sqrt{(4sqrt{2})^2+2^2}

$$\sqrt { ( 4 \sqrt { 2 } ) ^ { 2 } + 2 ^ { 2 } }$$

Evaluate

$$6$$

Solution Steps

Expand \left(4\sqrt{2}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16\left(\sqrt{2}\right)^{2}+2^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{16\times 2+2^{2}}$$

Multiply 16 and 2 to get 32.

$$\sqrt{32+2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{32+4}$$

Add 32 and 4 to get 36.

$$\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$6$$

Factor

$$2\times 3$$