Solve 2*sqrt{0.2440/9}=

$$2 \times \sqrt { \frac { 0.2440 } { 9 } } =$$

Evaluate

$$\frac{\sqrt{610}}{75}\approx 0.329309041$$

Solution Steps

Expand \frac{0.244}{9} by multiplying both numerator and the denominator by 1000.

$$2\sqrt{\frac{244}{9000}}$$

Reduce the fraction \frac{244}{9000} to lowest terms by extracting and canceling out 4.

$$2\sqrt{\frac{61}{2250}}$$

Rewrite the square root of the division \sqrt{\frac{61}{2250}} as the division of square roots \frac{\sqrt{61}}{\sqrt{2250}}.

$$2\times \frac{\sqrt{61}}{\sqrt{2250}}$$

Factor 2250=15^{2}\times 10. Rewrite the square root of the product \sqrt{15^{2}\times 10} as the product of square roots \sqrt{15^{2}}\sqrt{10}. Take the square root of 15^{2}.

$$2\times \frac{\sqrt{61}}{15\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{61}}{15\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$2\times \frac{\sqrt{61}\sqrt{10}}{15\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$2\times \frac{\sqrt{61}\sqrt{10}}{15\times 10}$$

To multiply \sqrt{61} and \sqrt{10}, multiply the numbers under the square root.

$$2\times \frac{\sqrt{610}}{15\times 10}$$

Multiply 15 and 10 to get 150.

$$2\times \frac{\sqrt{610}}{150}$$

Cancel out 150, the greatest common factor in 2 and 150.

$$\frac{\sqrt{610}}{75}$$