Solve 1/4sqrt{8}div2sqrt{1/2}*(-2sqrt{2})

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

Evaluate

$$-\frac{\sqrt{2}}{2}\approx -0.707106781$$

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}.

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

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

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

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

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

Divide \frac{1}{2}\sqrt{2} by 2 to get \frac{1}{4}\sqrt{2}.

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

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

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

Cancel out 2 and 2.

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

Multiply -\frac{1}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 2 to get 4.

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