Solve 7*sqrt{7div7000}

$$7 \times \sqrt{ 7 \div 7000 }$$

Evaluate

$$\frac{7\sqrt{10}}{100}\approx 0.221359436$$

Solution Steps

Reduce the fraction \frac{7}{7000} to lowest terms by extracting and canceling out 7.

$$7\sqrt{\frac{1}{1000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{1000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{1000}}.

$$7\times \frac{\sqrt{1}}{\sqrt{1000}}$$

Calculate the square root of 1 and get 1.

$$7\times \frac{1}{\sqrt{1000}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$7\times \frac{1}{10\sqrt{10}}$$

Rationalize the denominator of \frac{1}{10\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$7\times \frac{\sqrt{10}}{10\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$7\times \frac{\sqrt{10}}{10\times 10}$$

Multiply 10 and 10 to get 100.

$$7\times \frac{\sqrt{10}}{100}$$

Express 7\times \frac{\sqrt{10}}{100} as a single fraction.

$$\frac{7\sqrt{10}}{100}$$