Solve frac{4sqrt{2}}{8sqrt{10}}

$$\frac { 4 \sqrt { 2 } } { 8 \sqrt { 10 } }$$

Evaluate

$$\frac{\sqrt{5}}{10}\approx 0.223606798$$

Solution Steps

Cancel out 4 in both numerator and denominator.

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

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

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

The square of \sqrt{10} is 10.

$$\frac{\sqrt{2}\sqrt{10}}{2\times 10}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{5}}{2\times 10}$$

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

$$\frac{2\sqrt{5}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{2\sqrt{5}}{20}$$

Divide 2\sqrt{5} by 20 to get \frac{1}{10}\sqrt{5}.

$$\frac{1}{10}\sqrt{5}$$