Solve 2/sqrt{2}-sqrt{8}

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

Evaluate

$$-\sqrt{2}\approx -1.414213562$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$\sqrt{2}-\sqrt{8}$$

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}.

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

Combine \sqrt{2} and -2\sqrt{2} to get -\sqrt{2}.

$$-\sqrt{2}$$