Solve sqrt{27}-8sqrt{1/3}

$$\sqrt { 27 } - 8 \sqrt { \frac { 1 } { 3 } }$$

Evaluate

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

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}.

$$3\sqrt{3}-8\sqrt{\frac{1}{3}}$$

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

$$3\sqrt{3}-8\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$3\sqrt{3}-8\times \frac{1}{\sqrt{3}}$$

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

$$3\sqrt{3}-8\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

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

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

$$\frac{3\times 3\sqrt{3}}{3}+\frac{-8\sqrt{3}}{3}$$

Since \frac{3\times 3\sqrt{3}}{3} and \frac{-8\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 3\sqrt{3}-8\sqrt{3}.

$$\frac{9\sqrt{3}-8\sqrt{3}}{3}$$

Do the calculations in 9\sqrt{3}-8\sqrt{3}.

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