Solve sqrt{3/4-1/4*3}

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

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\sqrt{\frac{3}{4}-\frac{1}{12}}$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{1}{12} to fractions with denominator 12.

$$\sqrt{\frac{9}{12}-\frac{1}{12}}$$

Since \frac{9}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{9-1}{12}}$$

Subtract 1 from 9 to get 8.

$$\sqrt{\frac{8}{12}}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{2}{3}}$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3}$$