Solve sqrt{(-2)^2}+(-sqrt{4})*(-1/2)^-2-(1-sqrt{2})^0

$$\sqrt { ( - 2 ) ^ { 2 } } + ( - \sqrt { 4 } ) \times ( - \frac { 1 } { 2 } ) ^ { - 2 } - ( 1 - \sqrt { 2 } ) ^ { 0 }$$

Evaluate

$$-7$$

Solution Steps

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

$$\sqrt{4}+\left(-\sqrt{4}\right)\left(-\frac{1}{2}\right)^{-2}-\left(1-\sqrt{2}\right)^{0}$$

Calculate the square root of 4 and get 2.

$$2+\left(-\sqrt{4}\right)\left(-\frac{1}{2}\right)^{-2}-\left(1-\sqrt{2}\right)^{0}$$

Calculate the square root of 4 and get 2.

$$2-2\left(-\frac{1}{2}\right)^{-2}-\left(1-\sqrt{2}\right)^{0}$$

Calculate -\frac{1}{2} to the power of -2 and get 4.

$$2-2\times 4-\left(1-\sqrt{2}\right)^{0}$$

Multiply -2 and 4 to get -8.

$$2-8-\left(1-\sqrt{2}\right)^{0}$$

Subtract 8 from 2 to get -6.

$$-6-\left(1-\sqrt{2}\right)^{0}$$

Calculate 1-\sqrt{2} to the power of 0 and get 1.

$$-6-1$$

Subtract 1 from -6 to get -7.

$$-7$$

Factor

$$-7$$