Solve sqrt{(-2)^2}-4sqrt{1/2}

$$\sqrt { ( - 2 ) ^ { 2 } } - 4 \sqrt { \frac { 1 } { 2 } }$$

Evaluate

$$2-2\sqrt{2}\approx -0.828427125$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$\sqrt{4}-4\sqrt{\frac{1}{2}}$$

Calculate the square root of 4 and get 2.

$$2-4\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$2-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$2-4\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Cancel out 2, the greatest common factor in 4 and 2.

$$2-2\sqrt{2}$$