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

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

Evaluate

$$8$$

Solution Steps

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

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

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16\left(\sqrt{2}\right)^{2}+\left(4\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{16\times 2+\left(4\sqrt{2}\right)^{2}}$$

Multiply 16 and 2 to get 32.

$$\sqrt{32+\left(4\sqrt{2}\right)^{2}}$$

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

$$\sqrt{32+4^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{32+16\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{32+16\times 2}$$

Multiply 16 and 2 to get 32.

$$\sqrt{32+32}$$

Add 32 and 32 to get 64.

$$\sqrt{64}$$

Calculate the square root of 64 and get 8.

$$8$$

Factor

$$2^{3}$$