Solve 1/4sqrt{8}div(21/2)*(-2sqrt{2})

$$\frac { 1 } { 4 } \sqrt { 8 } \div ( 2 \frac { 1 } { 2 } ) \times ( - 2 \sqrt { 2 } )$$

Evaluate

$$-\frac{4}{5}=-0.8$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

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

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

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

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

$$\frac{\frac{1}{2}\sqrt{2}}{\frac{5}{2}}\left(-2\right)\sqrt{2}$$

Divide \frac{1}{2}\sqrt{2} by \frac{5}{2} by multiplying \frac{1}{2}\sqrt{2} by the reciprocal of \frac{5}{2}.

$$\frac{\frac{1}{2}\sqrt{2}\times 2}{5}\left(-2\right)\sqrt{2}$$

Cancel out 2 and 2.

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

Express \frac{\sqrt{2}}{5}\left(-2\right) as a single fraction.

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

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

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

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

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

Multiply -2 and 2 to get -4.

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

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

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

Factor

$$-\frac{4}{5} = -0.8$$