Solve sqrt{0.00001648div5}

$$\sqrt{ 0.00001648 \div 5 }$$

Evaluate

$$\frac{\sqrt{515}}{12500}\approx 0.001815489$$

Solution Steps

Expand \frac{0.00001648}{5} by multiplying both numerator and the denominator by 100000000.

$$\sqrt{\frac{1648}{500000000}}$$

Reduce the fraction \frac{1648}{500000000} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{103}{31250000}}$$

Rewrite the square root of the division \sqrt{\frac{103}{31250000}} as the division of square roots \frac{\sqrt{103}}{\sqrt{31250000}}.

$$\frac{\sqrt{103}}{\sqrt{31250000}}$$

Factor 31250000=2500^{2}\times 5. Rewrite the square root of the product \sqrt{2500^{2}\times 5} as the product of square roots \sqrt{2500^{2}}\sqrt{5}. Take the square root of 2500^{2}.

$$\frac{\sqrt{103}}{2500\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{103}}{2500\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{103}\sqrt{5}}{2500\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{103}\sqrt{5}}{2500\times 5}$$

To multiply \sqrt{103} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{515}}{2500\times 5}$$

Multiply 2500 and 5 to get 12500.

$$\frac{\sqrt{515}}{12500}$$