Solve sqrt{(-(-1)/2)^2+(-3/2)^2-2}

$$\sqrt { ( - \frac { ( - 1 ) } { 2 } ) ^ { 2 } + ( - \frac { 3 } { 2 } ) ^ { 2 } - 2 }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\sqrt{\left(-\left(-\frac{1}{2}\right)\right)^{2}+\left(-\frac{3}{2}\right)^{2}-2}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\sqrt{\left(\frac{1}{2}\right)^{2}+\left(-\frac{3}{2}\right)^{2}-2}$$

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

$$\sqrt{\frac{1}{4}+\left(-\frac{3}{2}\right)^{2}-2}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\sqrt{\frac{1}{4}+\frac{9}{4}-2}$$

Add \frac{1}{4} and \frac{9}{4} to get \frac{5}{2}.

$$\sqrt{\frac{5}{2}-2}$$

Subtract 2 from \frac{5}{2} to get \frac{1}{2}.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}$$