Solve sqrt{(4/7-1/2)^2}+sqrt{(4/7-1)^2}

$$\sqrt { ( \frac { 4 } { 7 } - \frac { 1 } { 2 } ) ^ { 2 } } + \sqrt { ( \frac { 4 } { 7 } - 1 ) ^ { 2 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Subtract \frac{1}{2} from \frac{4}{7} to get \frac{1}{14}.

$$\sqrt{\left(\frac{1}{14}\right)^{2}}+\sqrt{\left(\frac{4}{7}-1\right)^{2}}$$

Calculate \frac{1}{14} to the power of 2 and get \frac{1}{196}.

$$\sqrt{\frac{1}{196}}+\sqrt{\left(\frac{4}{7}-1\right)^{2}}$$

Rewrite the square root of the division \frac{1}{196} as the division of square roots \frac{\sqrt{1}}{\sqrt{196}}. Take the square root of both numerator and denominator.

$$\frac{1}{14}+\sqrt{\left(\frac{4}{7}-1\right)^{2}}$$

Subtract 1 from \frac{4}{7} to get -\frac{3}{7}.

$$\frac{1}{14}+\sqrt{\left(-\frac{3}{7}\right)^{2}}$$

Calculate -\frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{1}{14}+\sqrt{\frac{9}{49}}$$

Rewrite the square root of the division \frac{9}{49} as the division of square roots \frac{\sqrt{9}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$\frac{1}{14}+\frac{3}{7}$$

Add \frac{1}{14} and \frac{3}{7} to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$