Solve sqrt{27}-sqrt{12}+sqrt{7/3}

$$\sqrt { 27 } - \sqrt { 12 } + \sqrt { \frac { 7 } { 3 } }$$

Evaluate

$$\frac{\sqrt{21}}{3}+\sqrt{3}\approx 3.259576039$$

Short Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\sqrt{3}-\sqrt{12}+\sqrt{\frac{7}{3}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$3\sqrt{3}-2\sqrt{3}+\sqrt{\frac{7}{3}}$$

Combine 3\sqrt{3} and -2\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}+\sqrt{\frac{7}{3}}$$

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

$$\sqrt{3}+\frac{\sqrt{7}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}+\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{3}+\frac{\sqrt{7}\sqrt{3}}{3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\sqrt{3}+\frac{\sqrt{21}}{3}$$

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

$$\frac{3\sqrt{3}}{3}+\frac{\sqrt{21}}{3}$$

Since \frac{3\sqrt{3}}{3} and \frac{\sqrt{21}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{3}+\sqrt{21}}{3}$$