Solve sqrt{1/4}+sqrt{0.5^2}-sqrt[3]{1-18/27}

$$\sqrt { \frac { 1 } { 4 } } + \sqrt { 0.5 ^ { 2 } } - \sqrt[ 3 ] { 1 - 1 \frac { 8 } { 27 } }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}+\sqrt{0.5^{2}}-\sqrt[3]{1-\frac{1\times 27+8}{27}}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{1}{2}+\sqrt{0.25}-\sqrt[3]{1-\frac{1\times 27+8}{27}}$$

Calculate the square root of 0.25 and get 0.5.

$$\frac{1}{2}+0.5-\sqrt[3]{1-\frac{1\times 27+8}{27}}$$

Add \frac{1}{2} and 0.5 to get 1.

$$1-\sqrt[3]{1-\frac{1\times 27+8}{27}}$$

Multiply 1 and 27 to get 27.

$$1-\sqrt[3]{1-\frac{27+8}{27}}$$

Add 27 and 8 to get 35.

$$1-\sqrt[3]{1-\frac{35}{27}}$$

Subtract \frac{35}{27} from 1 to get -\frac{8}{27}.

$$1-\sqrt[3]{-\frac{8}{27}}$$

Calculate \sqrt[3]{-\frac{8}{27}} and get -\frac{2}{3}.

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

The opposite of -\frac{2}{3} is \frac{2}{3}.

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

Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$