Solve sqrt{7/800}

$$\sqrt { \frac { 7 } { 800 } }$$

Evaluate

$$\frac{\sqrt{14}}{40}\approx 0.093541435$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{800}} as the division of square roots \frac{\sqrt{7}}{\sqrt{800}}.

$$\frac{\sqrt{7}}{\sqrt{800}}$$

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$\frac{\sqrt{7}}{20\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7}}{20\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{7}\sqrt{2}}{20\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{7}\sqrt{2}}{20\times 2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{14}}{20\times 2}$$

Multiply 20 and 2 to get 40.

$$\frac{\sqrt{14}}{40}$$