Solve sqrt{left(12-1right)(125292.09)/26.757}

$$\sqrt{ \frac{ \left( 12-1 \right) (125292.09) }{ 26.757 } }$$

Evaluate

$$\frac{11\sqrt{3762559430}}{2973}\approx 226.954845893$$

Solution Steps

Subtract 1 from 12 to get 11.

$$\sqrt{\frac{11\times 125292.09}{26.757}}$$

Multiply 11 and 125292.09 to get 1378212.99.

$$\sqrt{\frac{1378212.99}{26.757}}$$

Expand \frac{1378212.99}{26.757} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1378212990}{26757}}$$

Reduce the fraction \frac{1378212990}{26757} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{459404330}{8919}}$$

Rewrite the square root of the division \sqrt{\frac{459404330}{8919}} as the division of square roots \frac{\sqrt{459404330}}{\sqrt{8919}}.

$$\frac{\sqrt{459404330}}{\sqrt{8919}}$$

Factor 459404330=11^{2}\times 3796730. Rewrite the square root of the product \sqrt{11^{2}\times 3796730} as the product of square roots \sqrt{11^{2}}\sqrt{3796730}. Take the square root of 11^{2}.

$$\frac{11\sqrt{3796730}}{\sqrt{8919}}$$

Factor 8919=3^{2}\times 991. Rewrite the square root of the product \sqrt{3^{2}\times 991} as the product of square roots \sqrt{3^{2}}\sqrt{991}. Take the square root of 3^{2}.

$$\frac{11\sqrt{3796730}}{3\sqrt{991}}$$

Rationalize the denominator of \frac{11\sqrt{3796730}}{3\sqrt{991}} by multiplying numerator and denominator by \sqrt{991}.

$$\frac{11\sqrt{3796730}\sqrt{991}}{3\left(\sqrt{991}\right)^{2}}$$

The square of \sqrt{991} is 991.

$$\frac{11\sqrt{3796730}\sqrt{991}}{3\times 991}$$

To multiply \sqrt{3796730} and \sqrt{991}, multiply the numbers under the square root.

$$\frac{11\sqrt{3762559430}}{3\times 991}$$

Multiply 3 and 991 to get 2973.

$$\frac{11\sqrt{3762559430}}{2973}$$