Solve sqrt{3/8+1/4+1/2/(1+frac{1{2})^2:(1-frac{1}{2})}}=

$$\sqrt { \frac { \frac { 3 } { 8 } + \frac { 1 } { 4 } + \frac { 1 } { 2 } } { ( 1 + \frac { 1 } { 2 } ) ^ { 2 } : ( 1 - \frac { 1 } { 2 } ) } } =$$

Evaluate

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

Solution Steps

Add \frac{3}{8} and \frac{1}{4} to get \frac{5}{8}.

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

Add \frac{5}{8} and \frac{1}{2} to get \frac{9}{8}.

$$\sqrt{\frac{\frac{9}{8}}{\frac{\left(1+\frac{1}{2}\right)^{2}}{1-\frac{1}{2}}}}$$

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

$$\sqrt{\frac{\frac{9}{8}}{\frac{\left(\frac{3}{2}\right)^{2}}{1-\frac{1}{2}}}}$$

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

$$\sqrt{\frac{\frac{9}{8}}{\frac{\frac{9}{4}}{1-\frac{1}{2}}}}$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\sqrt{\frac{\frac{9}{8}}{\frac{\frac{9}{4}}{\frac{1}{2}}}}$$

Divide \frac{9}{4} by \frac{1}{2} by multiplying \frac{9}{4} by the reciprocal of \frac{1}{2}.

$$\sqrt{\frac{\frac{9}{8}}{\frac{9}{4}\times 2}}$$

Multiply \frac{9}{4} and 2 to get \frac{9}{2}.

$$\sqrt{\frac{\frac{9}{8}}{\frac{9}{2}}}$$

Divide \frac{9}{8} by \frac{9}{2} by multiplying \frac{9}{8} by the reciprocal of \frac{9}{2}.

$$\sqrt{\frac{9}{8}\times \frac{2}{9}}$$

Multiply \frac{9}{8} and \frac{2}{9} to get \frac{1}{4}.

$$\sqrt{\frac{1}{4}}$$

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.

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

Factor

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