Solve sqrt{666/985*211}*688

$$\sqrt { \frac { 666 } { 985 } \times 211 } \times 688$$

Evaluate

$$\frac{2064\sqrt{15379790}}{985}\approx 8217.669395788$$

Solution Steps

Express \frac{666}{985}\times 211 as a single fraction.

$$688\sqrt{\frac{666\times 211}{985}}$$

Multiply 666 and 211 to get 140526.

$$688\sqrt{\frac{140526}{985}}$$

Rewrite the square root of the division \sqrt{\frac{140526}{985}} as the division of square roots \frac{\sqrt{140526}}{\sqrt{985}}.

$$688\times \frac{\sqrt{140526}}{\sqrt{985}}$$

Factor 140526=3^{2}\times 15614. Rewrite the square root of the product \sqrt{3^{2}\times 15614} as the product of square roots \sqrt{3^{2}}\sqrt{15614}. Take the square root of 3^{2}.

$$688\times \frac{3\sqrt{15614}}{\sqrt{985}}$$

Rationalize the denominator of \frac{3\sqrt{15614}}{\sqrt{985}} by multiplying numerator and denominator by \sqrt{985}.

$$688\times \frac{3\sqrt{15614}\sqrt{985}}{\left(\sqrt{985}\right)^{2}}$$

The square of \sqrt{985} is 985.

$$688\times \frac{3\sqrt{15614}\sqrt{985}}{985}$$

To multiply \sqrt{15614} and \sqrt{985}, multiply the numbers under the square root.

$$688\times \frac{3\sqrt{15379790}}{985}$$

Express 688\times \frac{3\sqrt{15379790}}{985} as a single fraction.

$$\frac{688\times 3\sqrt{15379790}}{985}$$

Multiply 688 and 3 to get 2064.

$$\frac{2064\sqrt{15379790}}{985}$$