Solve frac{sqrt{3.2}}{sqrt{0.2}}

$$\frac{ \sqrt{ 3.2 } }{ \sqrt{ 0.2 } }$$

Evaluate

$$4$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{3.2}}{\sqrt{0.2}} by multiplying numerator and denominator by \sqrt{0.2}.

$$\frac{\sqrt{3.2}\sqrt{0.2}}{\left(\sqrt{0.2}\right)^{2}}$$

The square of \sqrt{0.2} is 0.2.

$$\frac{\sqrt{3.2}\sqrt{0.2}}{0.2}$$

To multiply \sqrt{3.2} and \sqrt{0.2}, multiply the numbers under the square root.

$$\frac{\sqrt{0.64}}{0.2}$$

Calculate the square root of 0.64 and get 0.8.

$$\frac{0.8}{0.2}$$

Expand \frac{0.8}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$4$$

Factor

$$2^{2}$$