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

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

Evaluate

$$\frac{17}{3}\approx 5.666666667$$

Solution Steps

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{\frac{3}{4}}{\left(\frac{1}{2}\right)^{3}}-\frac{1}{3}$$

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

$$\frac{\frac{3}{4}}{\frac{1}{8}}-\frac{1}{3}$$

Divide \frac{3}{4} by \frac{1}{8} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{8}.

$$\frac{3}{4}\times 8-\frac{1}{3}$$

Express \frac{3}{4}\times 8 as a single fraction.

$$\frac{3\times 8}{4}-\frac{1}{3}$$

Multiply 3 and 8 to get 24.

$$\frac{24}{4}-\frac{1}{3}$$

Divide 24 by 4 to get 6.

$$6-\frac{1}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{18}{3}-\frac{1}{3}$$

Since \frac{18}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-1}{3}$$

Subtract 1 from 18 to get 17.

$$\frac{17}{3}$$

Factor

$$\frac{17}{3} = 5\frac{2}{3} = 5.666666666666667$$