Solve sqrt{2*0.196/10}

$$\sqrt { \frac { 2 \times 0.196 } { 10 } }$$

Evaluate

$$\frac{7\sqrt{2}}{50}\approx 0.197989899$$

Solution Steps

Multiply 2 and 0.196 to get 0.392.

$$\sqrt{\frac{0.392}{10}}$$

Expand \frac{0.392}{10} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{392}{10000}}$$

Reduce the fraction \frac{392}{10000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{49}{1250}}$$

Rewrite the square root of the division \sqrt{\frac{49}{1250}} as the division of square roots \frac{\sqrt{49}}{\sqrt{1250}}.

$$\frac{\sqrt{49}}{\sqrt{1250}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{1250}}$$

Factor 1250=25^{2}\times 2. Rewrite the square root of the product \sqrt{25^{2}\times 2} as the product of square roots \sqrt{25^{2}}\sqrt{2}. Take the square root of 25^{2}.

$$\frac{7}{25\sqrt{2}}$$

Rationalize the denominator of \frac{7}{25\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7\sqrt{2}}{25\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{7\sqrt{2}}{25\times 2}$$

Multiply 25 and 2 to get 50.

$$\frac{7\sqrt{2}}{50}$$