Solve (sqrt{2}-sqrt{8})(sqrt{2}-sqrt{8})

$$( \sqrt { 2 } - \sqrt { 8 } ) ( \sqrt { 2 } - \sqrt { 8 } )$$

Evaluate

$$2$$

Solution Steps

Multiply \sqrt{2}-\sqrt{8} and \sqrt{2}-\sqrt{8} to get \left(\sqrt{2}-\sqrt{8}\right)^{2}.

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

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\left(\sqrt{2}-2\sqrt{2}\right)^{2}$$

Combine \sqrt{2} and -2\sqrt{2} to get -\sqrt{2}.

$$\left(-\sqrt{2}\right)^{2}$$

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

$$\left(-1\right)^{2}\left(\sqrt{2}\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$1\times 2$$

Multiply 1 and 2 to get 2.

$$2$$

Factor

$$2$$