Solve sqrt{0.0048*0.87/0.027*0.04}

$$\sqrt { \frac { 0.0048 \times 0.87 } { 0.027 \times 0.04 } }$$

Evaluate

$$\frac{\sqrt{870}}{15}\approx 1.966384161$$

Solution Steps

Multiply 0.0048 and 0.87 to get 0.004176.

$$\sqrt{\frac{0.004176}{0.027\times 0.04}}$$

Multiply 0.027 and 0.04 to get 0.00108.

$$\sqrt{\frac{0.004176}{0.00108}}$$

Expand \frac{0.004176}{0.00108} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{4176}{1080}}$$

Reduce the fraction \frac{4176}{1080} to lowest terms by extracting and canceling out 72.

$$\sqrt{\frac{58}{15}}$$

Rewrite the square root of the division \sqrt{\frac{58}{15}} as the division of square roots \frac{\sqrt{58}}{\sqrt{15}}.

$$\frac{\sqrt{58}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{58}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{58}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{58}\sqrt{15}}{15}$$

To multiply \sqrt{58} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{870}}{15}$$