Solve -5sqrt{2}1/2sqrt{2}

$$- 5 \sqrt { 2 } \frac { 1 } { 2 \sqrt { 2 } }$$

Evaluate

$$-\frac{5}{2}=-2.5$$

Solution Steps

Rationalize the denominator of \frac{1}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$-5\sqrt{2}\times \frac{\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$-5\sqrt{2}\times \frac{\sqrt{2}}{4}$$

Express -5\times \frac{\sqrt{2}}{4} as a single fraction.

$$\frac{-5\sqrt{2}}{4}\sqrt{2}$$

Express \frac{-5\sqrt{2}}{4}\sqrt{2} as a single fraction.

$$\frac{-5\sqrt{2}\sqrt{2}}{4}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{-5\times 2}{4}$$

Multiply -5 and 2 to get -10.

$$\frac{-10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{2}$$

Factor

$$-\frac{5}{2} = -2\frac{1}{2} = -2.5$$