Solve 4sqrt{frac{1/256}+2}{3}

$$\frac { 4 \sqrt { \frac { 1 } { 256 } } + 2 } { 3 }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Rewrite the square root of the division \frac{1}{256} as the division of square roots \frac{\sqrt{1}}{\sqrt{256}}. Take the square root of both numerator and denominator.

$$\frac{4\times \frac{1}{16}+2}{3}$$

Multiply 4 and \frac{1}{16} to get \frac{4}{16}.

$$\frac{\frac{4}{16}+2}{3}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{1}{4}+2}{3}$$

Convert 2 to fraction \frac{8}{4}.

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

Since \frac{1}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

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

Add 1 and 8 to get 9.

$$\frac{\frac{9}{4}}{3}$$

Express \frac{\frac{9}{4}}{3} as a single fraction.

$$\frac{9}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{9}{12}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$