Solve sqrt{0.477div100}

$$\sqrt{ 0.477 \div 100 }$$

Evaluate

$$\frac{3\sqrt{530}}{1000}\approx 0.069065187$$

Solution Steps

Expand \frac{0.477}{100} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{477}{100000}}$$

Rewrite the square root of the division \sqrt{\frac{477}{100000}} as the division of square roots \frac{\sqrt{477}}{\sqrt{100000}}.

$$\frac{\sqrt{477}}{\sqrt{100000}}$$

Factor 477=3^{2}\times 53. Rewrite the square root of the product \sqrt{3^{2}\times 53} as the product of square roots \sqrt{3^{2}}\sqrt{53}. Take the square root of 3^{2}.

$$\frac{3\sqrt{53}}{\sqrt{100000}}$$

Factor 100000=100^{2}\times 10. Rewrite the square root of the product \sqrt{100^{2}\times 10} as the product of square roots \sqrt{100^{2}}\sqrt{10}. Take the square root of 100^{2}.

$$\frac{3\sqrt{53}}{100\sqrt{10}}$$

Rationalize the denominator of \frac{3\sqrt{53}}{100\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\sqrt{53}\sqrt{10}}{100\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{3\sqrt{53}\sqrt{10}}{100\times 10}$$

To multiply \sqrt{53} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{3\sqrt{530}}{100\times 10}$$

Multiply 100 and 10 to get 1000.

$$\frac{3\sqrt{530}}{1000}$$