Solve sqrt{[1/4+(2-3/4)^2-(7/8+7/16)]^2*(2-frac{2}{3})^2}

$$\sqrt { [ \frac { 1 } { 4 } + ( 2 - \frac { 3 } { 4 } ) ^ { 2 } - ( \frac { 7 } { 8 } + \frac { 7 } { 16 } ) ] ^ { 2 } \cdot ( 2 - \frac { 2 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Subtract \frac{3}{4} from 2 to get \frac{5}{4}.

$$\sqrt{\left(\frac{1}{4}+\left(\frac{5}{4}\right)^{2}-\left(\frac{7}{8}+\frac{7}{16}\right)\right)^{2}\left(2-\frac{2}{3}\right)^{2}}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\sqrt{\left(\frac{1}{4}+\frac{25}{16}-\left(\frac{7}{8}+\frac{7}{16}\right)\right)^{2}\left(2-\frac{2}{3}\right)^{2}}$$

Add \frac{1}{4} and \frac{25}{16} to get \frac{29}{16}.

$$\sqrt{\left(\frac{29}{16}-\left(\frac{7}{8}+\frac{7}{16}\right)\right)^{2}\left(2-\frac{2}{3}\right)^{2}}$$

Add \frac{7}{8} and \frac{7}{16} to get \frac{21}{16}.

$$\sqrt{\left(\frac{29}{16}-\frac{21}{16}\right)^{2}\left(2-\frac{2}{3}\right)^{2}}$$

Subtract \frac{21}{16} from \frac{29}{16} to get \frac{1}{2}.

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Subtract \frac{2}{3} from 2 to get \frac{4}{3}.

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

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\sqrt{\frac{1}{4}\times \frac{16}{9}}$$

Multiply \frac{1}{4} and \frac{16}{9} to get \frac{4}{9}.

$$\sqrt{\frac{4}{9}}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$