Solve 10/sqrt{2}-frac{sqrt{8}}{2}

$$\frac { 10 } { \sqrt { 2 } } - \frac { \sqrt { 8 } } { 2 }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Rationalize the denominator of \frac{10}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{10\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{8}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{10\sqrt{2}}{2}-\frac{\sqrt{8}}{2}$$

Divide 10\sqrt{2} by 2 to get 5\sqrt{2}.

$$5\sqrt{2}-\frac{\sqrt{8}}{2}$$

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}.

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

Cancel out 2 and 2.

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

Combine 5\sqrt{2} and -\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}$$