Solve sqrt{2.22/1100*1.005*0.000006}

$$\sqrt{ \frac{ 2.22 }{ 1100 \times 1.005 \times 0.000006 } }$$

Evaluate

$$\frac{100\sqrt{163614}}{2211}\approx 18.294539771$$

Solution Steps

Multiply 1100 and 1.005 to get 1105.5.

$$\sqrt{\frac{2.22}{1105.5\times 0.000006}}$$

Multiply 1105.5 and 0.000006 to get 0.006633.

$$\sqrt{\frac{2.22}{0.006633}}$$

Expand \frac{2.22}{0.006633} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{2220000}{6633}}$$

Reduce the fraction \frac{2220000}{6633} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{740000}{2211}}$$

Rewrite the square root of the division \sqrt{\frac{740000}{2211}} as the division of square roots \frac{\sqrt{740000}}{\sqrt{2211}}.

$$\frac{\sqrt{740000}}{\sqrt{2211}}$$

Factor 740000=100^{2}\times 74. Rewrite the square root of the product \sqrt{100^{2}\times 74} as the product of square roots \sqrt{100^{2}}\sqrt{74}. Take the square root of 100^{2}.

$$\frac{100\sqrt{74}}{\sqrt{2211}}$$

Rationalize the denominator of \frac{100\sqrt{74}}{\sqrt{2211}} by multiplying numerator and denominator by \sqrt{2211}.

$$\frac{100\sqrt{74}\sqrt{2211}}{\left(\sqrt{2211}\right)^{2}}$$

The square of \sqrt{2211} is 2211.

$$\frac{100\sqrt{74}\sqrt{2211}}{2211}$$

To multiply \sqrt{74} and \sqrt{2211}, multiply the numbers under the square root.

$$\frac{100\sqrt{163614}}{2211}$$