Solve (2-sqrt{2})(1-sqrt{2})sqrt{2}

$$(2- \sqrt{ 2 } )(1- \sqrt{ 2 } ) \sqrt{ 2 }$$

Evaluate

$$2^{\frac{5}{2}}-6\approx -0.343145751$$

Solution Steps

Apply the distributive property by multiplying each term of 2-\sqrt{2} by each term of 1-\sqrt{2}.

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

Combine -2\sqrt{2} and -\sqrt{2} to get -3\sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Add 2 and 2 to get 4.

$$\left(4-3\sqrt{2}\right)\sqrt{2}$$

Use the distributive property to multiply 4-3\sqrt{2} by \sqrt{2}.

$$4\sqrt{2}-3\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$4\sqrt{2}-3\times 2$$

Multiply -3 and 2 to get -6.

$$4\sqrt{2}-6$$

Factor

$$2 {(2 \sqrt{2} - 3)} = -0.343145751$$