Solve sqrt{left(12-1right)(103429.24)/26.757}

$$\sqrt{ \frac{ \left( 12-1 \right) (103429.24) }{ 26.757 } }$$

Evaluate

$$\frac{2\sqrt{845611608930}}{8919}\approx 206.205051411$$

Solution Steps

Subtract 1 from 12 to get 11.

$$\sqrt{\frac{11\times 103429.24}{26.757}}$$

Multiply 11 and 103429.24 to get 1137721.64.

$$\sqrt{\frac{1137721.64}{26.757}}$$

Expand \frac{1137721.64}{26.757} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1137721640}{26757}}$$

Rewrite the square root of the division \sqrt{\frac{1137721640}{26757}} as the division of square roots \frac{\sqrt{1137721640}}{\sqrt{26757}}.

$$\frac{\sqrt{1137721640}}{\sqrt{26757}}$$

Factor 1137721640=2^{2}\times 284430410. Rewrite the square root of the product \sqrt{2^{2}\times 284430410} as the product of square roots \sqrt{2^{2}}\sqrt{284430410}. Take the square root of 2^{2}.

$$\frac{2\sqrt{284430410}}{\sqrt{26757}}$$

Factor 26757=3^{2}\times 2973. Rewrite the square root of the product \sqrt{3^{2}\times 2973} as the product of square roots \sqrt{3^{2}}\sqrt{2973}. Take the square root of 3^{2}.

$$\frac{2\sqrt{284430410}}{3\sqrt{2973}}$$

Rationalize the denominator of \frac{2\sqrt{284430410}}{3\sqrt{2973}} by multiplying numerator and denominator by \sqrt{2973}.

$$\frac{2\sqrt{284430410}\sqrt{2973}}{3\left(\sqrt{2973}\right)^{2}}$$

The square of \sqrt{2973} is 2973.

$$\frac{2\sqrt{284430410}\sqrt{2973}}{3\times 2973}$$

To multiply \sqrt{284430410} and \sqrt{2973}, multiply the numbers under the square root.

$$\frac{2\sqrt{845611608930}}{3\times 2973}$$

Multiply 3 and 2973 to get 8919.

$$\frac{2\sqrt{845611608930}}{8919}$$