Solve sqrt{3.870/300+3.870}

$$\sqrt{ \frac{ 3.870 }{ 300+3.870 } }$$

Evaluate

$$\frac{\sqrt{1306641}}{10129}\approx 0.1128526$$

Solution Steps

Add 300 and 3.87 to get 303.87.

$$\sqrt{\frac{3.87}{303.87}}$$

Expand \frac{3.87}{303.87} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{387}{30387}}$$

Reduce the fraction \frac{387}{30387} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{129}{10129}}$$

Rewrite the square root of the division \sqrt{\frac{129}{10129}} as the division of square roots \frac{\sqrt{129}}{\sqrt{10129}}.

$$\frac{\sqrt{129}}{\sqrt{10129}}$$

Rationalize the denominator of \frac{\sqrt{129}}{\sqrt{10129}} by multiplying numerator and denominator by \sqrt{10129}.

$$\frac{\sqrt{129}\sqrt{10129}}{\left(\sqrt{10129}\right)^{2}}$$

The square of \sqrt{10129} is 10129.

$$\frac{\sqrt{129}\sqrt{10129}}{10129}$$

To multiply \sqrt{129} and \sqrt{10129}, multiply the numbers under the square root.

$$\frac{\sqrt{1306641}}{10129}$$