Solve (32sqrt{2})^2+(3sqrt{2})^2=

$$( 32 \sqrt { 2 } ) ^ { 2 } + ( 3 \sqrt { 2 } ) ^ { 2 } =$$

Evaluate

$$2066$$

Solution Steps

Expand \left(32\sqrt{2}\right)^{2}.

$$32^{2}\left(\sqrt{2}\right)^{2}+\left(3\sqrt{2}\right)^{2}$$

Calculate 32 to the power of 2 and get 1024.

$$1024\left(\sqrt{2}\right)^{2}+\left(3\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$1024\times 2+\left(3\sqrt{2}\right)^{2}$$

Multiply 1024 and 2 to get 2048.

$$2048+\left(3\sqrt{2}\right)^{2}$$

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

$$2048+3^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$2048+9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2048+9\times 2$$

Multiply 9 and 2 to get 18.

$$2048+18$$

Add 2048 and 18 to get 2066.

$$2066$$

Factor

$$2\times 1033$$