Solve 16sqrt{3}-4sqrt{1/27}

$$16 \sqrt { 3 } - 4 \sqrt { \frac { 1 } { 27 } }$$

Evaluate

$$\frac{140\sqrt{3}}{9}\approx 26.943012562$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{27}} as the division of square roots \frac{\sqrt{1}}{\sqrt{27}}.

$$16\sqrt{3}-4\times \frac{\sqrt{1}}{\sqrt{27}}$$

Calculate the square root of 1 and get 1.

$$16\sqrt{3}-4\times \frac{1}{\sqrt{27}}$$

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}.

$$16\sqrt{3}-4\times \frac{1}{3\sqrt{3}}$$

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

$$16\sqrt{3}-4\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$16\sqrt{3}-4\times \frac{\sqrt{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$16\sqrt{3}-4\times \frac{\sqrt{3}}{9}$$

Express -4\times \frac{\sqrt{3}}{9} as a single fraction.

$$16\sqrt{3}+\frac{-4\sqrt{3}}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16\sqrt{3} times \frac{9}{9}.

$$\frac{9\times 16\sqrt{3}}{9}+\frac{-4\sqrt{3}}{9}$$

Since \frac{9\times 16\sqrt{3}}{9} and \frac{-4\sqrt{3}}{9} have the same denominator, add them by adding their numerators.

$$\frac{9\times 16\sqrt{3}-4\sqrt{3}}{9}$$

Do the multiplications in 9\times 16\sqrt{3}-4\sqrt{3}.

$$\frac{144\sqrt{3}-4\sqrt{3}}{9}$$

Do the calculations in 144\sqrt{3}-4\sqrt{3}.

$$\frac{140\sqrt{3}}{9}$$