Solve =-1/frac{1{4}}sqrt{frac{81/4}}{4}

$$= - \frac { 1 } { \frac { 1 } { 4 } } \frac { \sqrt { \frac { 81 } { 4 } } } { 4 }$$

Evaluate

$$-\frac{9}{2}=-4.5$$

Solution Steps

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

$$\left(-1\times 4\right)\times \frac{\sqrt{\frac{81}{4}}}{4}$$

Multiply 1 and 4 to get 4.

$$-4\times \frac{\sqrt{\frac{81}{4}}}{4}$$

Rewrite the square root of the division \frac{81}{4} as the division of square roots \frac{\sqrt{81}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-4\times \frac{\frac{9}{2}}{4}$$

Express \frac{\frac{9}{2}}{4} as a single fraction.

$$-4\times \frac{9}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$-4\times \frac{9}{8}$$

Express -4\times \frac{9}{8} as a single fraction.

$$\frac{-4\times 9}{8}$$

Multiply -4 and 9 to get -36.

$$\frac{-36}{8}$$

Reduce the fraction \frac{-36}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{9}{2}$$

Factor

$$-\frac{9}{2} = -4\frac{1}{2} = -4.5$$