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

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

Evaluate

$$\frac{9}{25}=0.36$$

Solution Steps

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

$$\left(\frac{\sqrt{\frac{9}{4}}}{-1-\frac{3}{2}}\right)^{2}$$

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.

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

Subtract \frac{3}{2} from -1 to get -\frac{5}{2}.

$$\left(\frac{\frac{3}{2}}{-\frac{5}{2}}\right)^{2}$$

Divide \frac{3}{2} by -\frac{5}{2} by multiplying \frac{3}{2} by the reciprocal of -\frac{5}{2}.

$$\left(\frac{3}{2}\left(-\frac{2}{5}\right)\right)^{2}$$

Multiply \frac{3}{2} and -\frac{2}{5} to get -\frac{3}{5}.

$$\left(-\frac{3}{5}\right)^{2}$$

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{9}{25}$$

Factor

$$\frac{3 ^ {2}}{5 ^ {2}} = 0.36$$