Solve sqrt{15.18/300+15.18}

$$\sqrt{ \frac{ 15.18 }{ 300+15.18 } }$$

Evaluate

$$\frac{\sqrt{1329009}}{5253}\approx 0.219460599$$

Solution Steps

Add 300 and 15.18 to get 315.18.

$$\sqrt{\frac{15.18}{315.18}}$$

Expand \frac{15.18}{315.18} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1518}{31518}}$$

Reduce the fraction \frac{1518}{31518} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{253}{5253}}$$

Rewrite the square root of the division \sqrt{\frac{253}{5253}} as the division of square roots \frac{\sqrt{253}}{\sqrt{5253}}.

$$\frac{\sqrt{253}}{\sqrt{5253}}$$

Rationalize the denominator of \frac{\sqrt{253}}{\sqrt{5253}} by multiplying numerator and denominator by \sqrt{5253}.

$$\frac{\sqrt{253}\sqrt{5253}}{\left(\sqrt{5253}\right)^{2}}$$

The square of \sqrt{5253} is 5253.

$$\frac{\sqrt{253}\sqrt{5253}}{5253}$$

To multiply \sqrt{253} and \sqrt{5253}, multiply the numbers under the square root.

$$\frac{\sqrt{1329009}}{5253}$$