Solve x/sqrt{2}frac{sqrt{8}}{x}

$$\frac{ x }{ \sqrt{ 2 } } \frac{ \sqrt{ 8 } }{ x }$$

Evaluate

$$2$$

Solution Steps

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

$$\frac{x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{8}}{x}$$

The square of \sqrt{2} is 2.

$$\frac{x\sqrt{2}}{2}\times \frac{\sqrt{8}}{x}$$

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}.

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

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

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

Cancel out 2x in both numerator and denominator.

$$\sqrt{2}\sqrt{2}$$

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

$$2$$

Factor

$$2$$