Solve 5/sqrt{2}-2/sqrt{8}

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

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Rationalize the denominator of \frac{5}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{2}{\sqrt{8}}$$

The square of \sqrt{2} is 2.

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

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}.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 in both numerator and denominator.

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

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

$$2\sqrt{2}$$