Solve sqrt{1}*222*222*222*222*222div222div222div22div22*2/frac{2{2}*2div525111}*2div2525222

$$\sqrt{ 1 } \times 222 \times 222 \times 222 \times 222 \times 222 \div 222 \div 222 \div 22 \div 22 \times \frac{ 2 }{ \frac{ 2 }{ 2 } \times 2 \div 525111 } \times 2 \div 2525222$$

Evaluate

$$\frac{1436316164082}{152775931}\approx 9401.455809698$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{2\times \frac{\frac{\frac{\frac{222\times 222\times 222\times 222\times 222\sqrt{1}}{222}}{222}}{22}}{22}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Express \frac{\frac{\frac{\frac{222\times 222\times 222\times 222\times 222\sqrt{1}}{222}}{222}}{22}}{22} as a single fraction.

$$\frac{2\times \frac{\frac{\frac{222\times 222\times 222\times 222\times 222\sqrt{1}}{222}}{222}}{22\times 22}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Express \frac{\frac{222\times 222\times 222\times 222\times 222\sqrt{1}}{222}}{222} as a single fraction.

$$\frac{2\times \frac{\frac{222\times 222\times 222\times 222\times 222\sqrt{1}}{222\times 222}}{22\times 22}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Cancel out 222\times 222 in both numerator and denominator.

$$\frac{2\times \frac{222\times 222\times 222\sqrt{1}}{22\times 22}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Multiply 222 and 222 to get 49284.

$$\frac{2\times \frac{49284\times 222\sqrt{1}}{22\times 22}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Multiply 49284 and 222 to get 10941048.

$$\frac{2\times \frac{10941048\sqrt{1}}{22\times 22}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Multiply 22 and 22 to get 484.

$$\frac{2\times \frac{10941048\sqrt{1}}{484}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Calculate the square root of 1 and get 1.

$$\frac{2\times \frac{10941048\times 1}{484}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Multiply 10941048 and 1 to get 10941048.

$$\frac{2\times \frac{10941048}{484}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Reduce the fraction \frac{10941048}{484} to lowest terms by extracting and canceling out 4.

$$\frac{2\times \frac{2735262}{121}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Express 2\times \frac{2735262}{121} as a single fraction.

$$\frac{\frac{2\times 2735262}{121}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Multiply 2 and 2735262 to get 5470524.

$$\frac{\frac{5470524}{121}\times \frac{2}{\frac{1\times 2}{525111}}}{2525222}$$

Divide 2 by \frac{1\times 2}{525111} by multiplying 2 by the reciprocal of \frac{1\times 2}{525111}.

$$\frac{\frac{5470524}{121}\times \frac{2\times 525111}{1\times 2}}{2525222}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{5470524}{121}\times 525111}{2525222}$$

Express \frac{5470524}{121}\times 525111 as a single fraction.

$$\frac{\frac{5470524\times 525111}{121}}{2525222}$$

Multiply 5470524 and 525111 to get 2872632328164.

$$\frac{\frac{2872632328164}{121}}{2525222}$$

Express \frac{\frac{2872632328164}{121}}{2525222} as a single fraction.

$$\frac{2872632328164}{121\times 2525222}$$

Multiply 121 and 2525222 to get 305551862.

$$\frac{2872632328164}{305551862}$$

Reduce the fraction \frac{2872632328164}{305551862} to lowest terms by extracting and canceling out 2.

$$\frac{1436316164082}{152775931}$$

Factor

$$\frac{2 \cdot 3 ^ {4} \cdot 37 ^ {3} \cdot 113 \cdot 1549}{7 \cdot 11 ^ {2} \cdot 317 \cdot 569} = 9401\frac{69636751}{152775931} = 9401.455809698191$$