Solve sqrt{13/6:[-(-1/2)^-1]^-1-3/9}

$$\sqrt { \frac { 13 } { 6 } : [ - ( - \frac { 1 } { 2 } ) ^ { - 1 } ] ^ { - 1 } - \frac { 3 } { 9 } }$$

Evaluate

$$2$$

Solution Steps

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

$$\sqrt{\frac{\frac{13}{6}}{\left(-\left(-2\right)\right)^{-1}}-\frac{3}{9}}$$

The opposite of -2 is 2.

$$\sqrt{\frac{\frac{13}{6}}{2^{-1}}-\frac{3}{9}}$$

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

$$\sqrt{\frac{\frac{13}{6}}{\frac{1}{2}}-\frac{3}{9}}$$

Divide \frac{13}{6} by \frac{1}{2} by multiplying \frac{13}{6} by the reciprocal of \frac{1}{2}.

$$\sqrt{\frac{13}{6}\times 2-\frac{3}{9}}$$

Multiply \frac{13}{6} and 2 to get \frac{13}{3}.

$$\sqrt{\frac{13}{3}-\frac{3}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{13}{3}-\frac{1}{3}}$$

Subtract \frac{1}{3} from \frac{13}{3} to get 4.

$$\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$2$$

Factor

$$2$$