Solve frac{sqrt{4}}{2sqrt{20}}

$$\frac { \sqrt { 4 } } { 2 \sqrt { 20 } }$$

Evaluate

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

Solution Steps

Calculate the square root of 4 and get 2.

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

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

$$\frac{2}{4\sqrt{5}}$$

Rationalize the denominator of \frac{2}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{5}}{4\times 5}$$

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 5 to get 10.

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