Solve sqrt{[25/8:(3/4+1-4/3)*2/15]^2+(frac{1}{2}+frac{3}{4})}

$$\sqrt { [ \frac { 25 } { 8 } : ( \frac { 3 } { 4 } + 1 - \frac { 4 } { 3 } ) \cdot \frac { 2 } { 15 } ] ^ { 2 } + ( \frac { 1 } { 2 } + \frac { 3 } { 4 } ) }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Add \frac{3}{4} and 1 to get \frac{7}{4}.

$$\sqrt{\left(\frac{\frac{25}{8}}{\frac{7}{4}-\frac{4}{3}}\times \frac{2}{15}\right)^{2}+\frac{1}{2}+\frac{3}{4}}$$

Subtract \frac{4}{3} from \frac{7}{4} to get \frac{5}{12}.

$$\sqrt{\left(\frac{\frac{25}{8}}{\frac{5}{12}}\times \frac{2}{15}\right)^{2}+\frac{1}{2}+\frac{3}{4}}$$

Divide \frac{25}{8} by \frac{5}{12} by multiplying \frac{25}{8} by the reciprocal of \frac{5}{12}.

$$\sqrt{\left(\frac{25}{8}\times \frac{12}{5}\times \frac{2}{15}\right)^{2}+\frac{1}{2}+\frac{3}{4}}$$

Multiply \frac{25}{8} and \frac{12}{5} to get \frac{15}{2}.

$$\sqrt{\left(\frac{15}{2}\times \frac{2}{15}\right)^{2}+\frac{1}{2}+\frac{3}{4}}$$

Multiply \frac{15}{2} and \frac{2}{15} to get 1.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

Add \frac{3}{2} and \frac{3}{4} to get \frac{9}{4}.

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

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

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

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$