Solve sqrt{4331/380}*100

$$\sqrt { \frac { 4331 } { 380 } } \times 100$$

Evaluate

$$\frac{10\sqrt{411445}}{19}\approx 337.599887753$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{4331}{380}} as the division of square roots \frac{\sqrt{4331}}{\sqrt{380}}.

$$100\times \frac{\sqrt{4331}}{\sqrt{380}}$$

Factor 380=2^{2}\times 95. Rewrite the square root of the product \sqrt{2^{2}\times 95} as the product of square roots \sqrt{2^{2}}\sqrt{95}. Take the square root of 2^{2}.

$$100\times \frac{\sqrt{4331}}{2\sqrt{95}}$$

Rationalize the denominator of \frac{\sqrt{4331}}{2\sqrt{95}} by multiplying numerator and denominator by \sqrt{95}.

$$100\times \frac{\sqrt{4331}\sqrt{95}}{2\left(\sqrt{95}\right)^{2}}$$

The square of \sqrt{95} is 95.

$$100\times \frac{\sqrt{4331}\sqrt{95}}{2\times 95}$$

To multiply \sqrt{4331} and \sqrt{95}, multiply the numbers under the square root.

$$100\times \frac{\sqrt{411445}}{2\times 95}$$

Multiply 2 and 95 to get 190.

$$100\times \frac{\sqrt{411445}}{190}$$

Express 100\times \frac{\sqrt{411445}}{190} as a single fraction.

$$\frac{100\sqrt{411445}}{190}$$

Divide 100\sqrt{411445} by 190 to get \frac{10}{19}\sqrt{411445}.

$$\frac{10}{19}\sqrt{411445}$$