Solve sqrt{0.0184div9}

$$\sqrt{ 0.0184 \div 9 }$$

Evaluate

$$\frac{\sqrt{46}}{150}\approx 0.045215533$$

Solution Steps

Expand \frac{0.0184}{9} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{184}{90000}}$$

Reduce the fraction \frac{184}{90000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{23}{11250}}$$

Rewrite the square root of the division \sqrt{\frac{23}{11250}} as the division of square roots \frac{\sqrt{23}}{\sqrt{11250}}.

$$\frac{\sqrt{23}}{\sqrt{11250}}$$

Factor 11250=75^{2}\times 2. Rewrite the square root of the product \sqrt{75^{2}\times 2} as the product of square roots \sqrt{75^{2}}\sqrt{2}. Take the square root of 75^{2}.

$$\frac{\sqrt{23}}{75\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{23}}{75\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{23}\sqrt{2}}{75\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{23}\sqrt{2}}{75\times 2}$$

To multiply \sqrt{23} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{46}}{75\times 2}$$

Multiply 75 and 2 to get 150.

$$\frac{\sqrt{46}}{150}$$