Solve frac{sqrt{0.02}*sqrt{80}}{sqrt{0.9}}

$$\frac { \sqrt { 0.02 } \times \sqrt { 80 } } { \sqrt { 0.9 } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{\sqrt{0.02}\times 4\sqrt{5}}{\sqrt{0.9}}$$

To multiply \sqrt{0.02} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{0.1}\times 4}{\sqrt{0.9}}$$

Rationalize the denominator of \frac{\sqrt{0.1}\times 4}{\sqrt{0.9}} by multiplying numerator and denominator by \sqrt{0.9}.

$$\frac{\sqrt{0.1}\times 4\sqrt{0.9}}{\left(\sqrt{0.9}\right)^{2}}$$

The square of \sqrt{0.9} is 0.9.

$$\frac{\sqrt{0.1}\times 4\sqrt{0.9}}{0.9}$$

To multiply \sqrt{0.1} and \sqrt{0.9}, multiply the numbers under the square root.

$$\frac{\sqrt{0.09}\times 4}{0.9}$$

Calculate the square root of 0.09 and get 0.3.

$$\frac{0.3\times 4}{0.9}$$

Multiply 0.3 and 4 to get 1.2.

$$\frac{1.2}{0.9}$$

Expand \frac{1.2}{0.9} by multiplying both numerator and the denominator by 10.

$$\frac{12}{9}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$