Solve sqrt{17380/.5067*451}

$$\sqrt{ \frac{ 17380 }{ .5067 \times 451 } }$$

Evaluate

$$\frac{200\sqrt{9117785}}{69249}\approx 8.720897116$$

Solution Steps

Multiply 0.5067 and 451 to get 228.5217.

$$\sqrt{\frac{17380}{228.5217}}$$

Expand \frac{17380}{228.5217} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{173800000}{2285217}}$$

Reduce the fraction \frac{173800000}{2285217} to lowest terms by extracting and canceling out 11.

$$\sqrt{\frac{15800000}{207747}}$$

Rewrite the square root of the division \sqrt{\frac{15800000}{207747}} as the division of square roots \frac{\sqrt{15800000}}{\sqrt{207747}}.

$$\frac{\sqrt{15800000}}{\sqrt{207747}}$$

Factor 15800000=200^{2}\times 395. Rewrite the square root of the product \sqrt{200^{2}\times 395} as the product of square roots \sqrt{200^{2}}\sqrt{395}. Take the square root of 200^{2}.

$$\frac{200\sqrt{395}}{\sqrt{207747}}$$

Factor 207747=3^{2}\times 23083. Rewrite the square root of the product \sqrt{3^{2}\times 23083} as the product of square roots \sqrt{3^{2}}\sqrt{23083}. Take the square root of 3^{2}.

$$\frac{200\sqrt{395}}{3\sqrt{23083}}$$

Rationalize the denominator of \frac{200\sqrt{395}}{3\sqrt{23083}} by multiplying numerator and denominator by \sqrt{23083}.

$$\frac{200\sqrt{395}\sqrt{23083}}{3\left(\sqrt{23083}\right)^{2}}$$

The square of \sqrt{23083} is 23083.

$$\frac{200\sqrt{395}\sqrt{23083}}{3\times 23083}$$

To multiply \sqrt{395} and \sqrt{23083}, multiply the numbers under the square root.

$$\frac{200\sqrt{9117785}}{3\times 23083}$$

Multiply 3 and 23083 to get 69249.

$$\frac{200\sqrt{9117785}}{69249}$$