Solve sqrt{{left(1/2right)}^-2{left(-1-1/2right)}^2}

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

Evaluate

$$3$$

Solution Steps

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

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

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

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

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

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

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

$$\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$3$$

Factor

$$3$$