Solve left(sqrt{27}-sqrt{1/3}right)*sqrt{3}

$$\left( \sqrt{ 27 } - \sqrt{ \frac{ 1 }{ 3 } } \right) \times \sqrt{ 3 }$$

Evaluate

$$8$$

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}.

$$\left(3\sqrt{3}-\sqrt{\frac{1}{3}}\right)\sqrt{3}$$

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

$$\left(3\sqrt{3}-\frac{\sqrt{1}}{\sqrt{3}}\right)\sqrt{3}$$

Calculate the square root of 1 and get 1.

$$\left(3\sqrt{3}-\frac{1}{\sqrt{3}}\right)\sqrt{3}$$

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

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

The square of \sqrt{3} is 3.

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

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

$$\left(\frac{3\times 3\sqrt{3}}{3}-\frac{\sqrt{3}}{3}\right)\sqrt{3}$$

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

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

Do the multiplications in 3\times 3\sqrt{3}-\sqrt{3}.

$$\frac{9\sqrt{3}-\sqrt{3}}{3}\sqrt{3}$$

Do the calculations in 9\sqrt{3}-\sqrt{3}.

$$\frac{8\sqrt{3}}{3}\sqrt{3}$$

Express \frac{8\sqrt{3}}{3}\sqrt{3} as a single fraction.

$$\frac{8\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{8\times 3}{3}$$

Cancel out 3 and 3.

$$8$$

Factor

$$2^{3}$$