Solve sqrt{-1div2+1}

$$\sqrt{ -1 \div 2+1 }$$

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.

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

Convert 1 to fraction \frac{2}{2}.

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

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 2 to get 1.

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

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.

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