Solve 196(sqrt{306*694/2258})

$$196 ( \sqrt { \frac { 306 \times 694 } { 2258 } } )$$

Evaluate

$$\frac{588\sqrt{13319942}}{1129}\approx 1900.791805549$$

Solution Steps

Multiply 306 and 694 to get 212364.

$$196\sqrt{\frac{212364}{2258}}$$

Reduce the fraction \frac{212364}{2258} to lowest terms by extracting and canceling out 2.

$$196\sqrt{\frac{106182}{1129}}$$

Rewrite the square root of the division \sqrt{\frac{106182}{1129}} as the division of square roots \frac{\sqrt{106182}}{\sqrt{1129}}.

$$196\times \frac{\sqrt{106182}}{\sqrt{1129}}$$

Factor 106182=3^{2}\times 11798. Rewrite the square root of the product \sqrt{3^{2}\times 11798} as the product of square roots \sqrt{3^{2}}\sqrt{11798}. Take the square root of 3^{2}.

$$196\times \frac{3\sqrt{11798}}{\sqrt{1129}}$$

Rationalize the denominator of \frac{3\sqrt{11798}}{\sqrt{1129}} by multiplying numerator and denominator by \sqrt{1129}.

$$196\times \frac{3\sqrt{11798}\sqrt{1129}}{\left(\sqrt{1129}\right)^{2}}$$

The square of \sqrt{1129} is 1129.

$$196\times \frac{3\sqrt{11798}\sqrt{1129}}{1129}$$

To multiply \sqrt{11798} and \sqrt{1129}, multiply the numbers under the square root.

$$196\times \frac{3\sqrt{13319942}}{1129}$$

Express 196\times \frac{3\sqrt{13319942}}{1129} as a single fraction.

$$\frac{196\times 3\sqrt{13319942}}{1129}$$

Multiply 196 and 3 to get 588.

$$\frac{588\sqrt{13319942}}{1129}$$