Solve frac{sqrt{28,8}}{sqrt{20}}

$$\frac { \sqrt { 28,8 } } { \sqrt { 20 } }$$

Evaluate

$$1,2$$

Solution Steps

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}.

$$\frac{\sqrt{28,8}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{28,8}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{28,8}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{28,8}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{28,8} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{144}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{144}}{10}$$

Calculate the square root of 144 and get 12.

$$\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$