Solve 6sqrt{1/3}-sqrt{27}=

$$6 \sqrt { \frac { 1 } { 3 } } - \sqrt { 27 } =$$

Evaluate

$$-\sqrt{3}\approx -1.732050808$$

Solution Steps

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

$$6\times \frac{\sqrt{1}}{\sqrt{3}}-\sqrt{27}$$

Calculate the square root of 1 and get 1.

$$6\times \frac{1}{\sqrt{3}}-\sqrt{27}$$

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

$$6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{27}$$

The square of \sqrt{3} is 3.

$$6\times \frac{\sqrt{3}}{3}-\sqrt{27}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$2\sqrt{3}-\sqrt{27}$$

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}.

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

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

$$-\sqrt{3}$$