Solve sqrt{1+-1/3/2}

$$\sqrt{ \frac{ 1+ \frac{ -1 }{ 3 } }{ 2 } }$$

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\sqrt{\frac{1-\frac{1}{3}}{2}}$$

Convert 1 to fraction \frac{3}{3}.

$$\sqrt{\frac{\frac{3}{3}-\frac{1}{3}}{2}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{3-1}{3}}{2}}$$

Subtract 1 from 3 to get 2.

$$\sqrt{\frac{\frac{2}{3}}{2}}$$

Express \frac{\frac{2}{3}}{2} as a single fraction.

$$\sqrt{\frac{2}{3\times 2}}$$

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{3}$$