Solve sqrt{1/3}-3+2

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

Evaluate

$$\frac{\sqrt{3}}{3}-1\approx -0.422649731$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Add -3 and 2 to get -1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

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

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

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