Solve sqrt{66*134/3131}

$$\sqrt { \frac { 66 \cdot 134 } { 3131 } }$$

Evaluate

$$\frac{2\sqrt{6922641}}{3131}\approx 1.680671491$$

Solution Steps

Multiply 66 and 134 to get 8844.

$$\sqrt{\frac{8844}{3131}}$$

Rewrite the square root of the division \sqrt{\frac{8844}{3131}} as the division of square roots \frac{\sqrt{8844}}{\sqrt{3131}}.

$$\frac{\sqrt{8844}}{\sqrt{3131}}$$

Factor 8844=2^{2}\times 2211. Rewrite the square root of the product \sqrt{2^{2}\times 2211} as the product of square roots \sqrt{2^{2}}\sqrt{2211}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2211}}{\sqrt{3131}}$$

Rationalize the denominator of \frac{2\sqrt{2211}}{\sqrt{3131}} by multiplying numerator and denominator by \sqrt{3131}.

$$\frac{2\sqrt{2211}\sqrt{3131}}{\left(\sqrt{3131}\right)^{2}}$$

The square of \sqrt{3131} is 3131.

$$\frac{2\sqrt{2211}\sqrt{3131}}{3131}$$

To multiply \sqrt{2211} and \sqrt{3131}, multiply the numbers under the square root.

$$\frac{2\sqrt{6922641}}{3131}$$