Solve sqrt[3]{27}-sqrt[3]{1/64}:sqrt{3}

$$\sqrt[ 3 ] { 27 } - \sqrt[ 3 ] { \frac { 1 } { 64 } } : \sqrt { 3 }$$

Evaluate

$$-\frac{\sqrt{3}}{12}+3\approx 2.855662433$$

Short Solution Steps

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

$$3-\frac{\sqrt[3]{\frac{1}{64}}}{\sqrt{3}}$$

Calculate \sqrt[3]{\frac{1}{64}} and get \frac{1}{4}.

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

Express \frac{\frac{1}{4}}{\sqrt{3}} as a single fraction.

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

Rationalize the denominator of \frac{1}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$3-\frac{\sqrt{3}}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{12}{12}.

$$\frac{3\times 12}{12}-\frac{\sqrt{3}}{12}$$

Since \frac{3\times 12}{12} and \frac{\sqrt{3}}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 12-\sqrt{3}}{12}$$

Do the multiplications in 3\times 12-\sqrt{3}.

$$\frac{36-\sqrt{3}}{12}$$