Solve sqrt{{left(frac{-sqrt{2}}{2}right)}^2+{left(frac{-sqrt{2}}{2}right)}^2}

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

Evaluate

$$1$$

Solution Steps

To raise \frac{-\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{-\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Combine \frac{\left(-\sqrt{2}\right)^{2}}{2^{2}} and \frac{\left(-\sqrt{2}\right)^{2}}{2^{2}} to get 2\times \frac{\left(-\sqrt{2}\right)^{2}}{2^{2}}.

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

Calculate -\sqrt{2} to the power of 2 and get \left(\sqrt{2}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{2} is 2.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Multiply 2 and \frac{1}{2} to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$