Solve sqrt{9/16div(1/2)^3-1/3}

$$\sqrt { \frac { 9 } { 16 } \div ( \frac { 1 } { 2 } ) ^ { 3 } - \frac { 1 } { 3 } }$$

Evaluate

$$\frac{5\sqrt{6}}{6}\approx 2.041241452$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\sqrt{\frac{\frac{9}{16}}{\frac{1}{8}}-\frac{1}{3}}$$

Divide \frac{9}{16} by \frac{1}{8} by multiplying \frac{9}{16} by the reciprocal of \frac{1}{8}.

$$\sqrt{\frac{9}{16}\times 8-\frac{1}{3}}$$

Express \frac{9}{16}\times 8 as a single fraction.

$$\sqrt{\frac{9\times 8}{16}-\frac{1}{3}}$$

Multiply 9 and 8 to get 72.

$$\sqrt{\frac{72}{16}-\frac{1}{3}}$$

Reduce the fraction \frac{72}{16} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{9}{2}-\frac{1}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{1}{3} to fractions with denominator 6.

$$\sqrt{\frac{27}{6}-\frac{2}{6}}$$

Since \frac{27}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{27-2}{6}}$$

Subtract 2 from 27 to get 25.

$$\sqrt{\frac{25}{6}}$$

Rewrite the square root of the division \sqrt{\frac{25}{6}} as the division of square roots \frac{\sqrt{25}}{\sqrt{6}}.

$$\frac{\sqrt{25}}{\sqrt{6}}$$

Calculate the square root of 25 and get 5.

$$\frac{5}{\sqrt{6}}$$

Rationalize the denominator of \frac{5}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{5\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{5\sqrt{6}}{6}$$