Solve sqrt[3]{27}-3sqrt{1/3}

$$\sqrt[ 3 ] { 27 } - 3 \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$3-\sqrt{3}\approx 1.267949192$$

Solution Steps

Calculate \sqrt[3]{27} and get 3.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

$$3-\sqrt{3}$$