Solve 1/2*165frac{0.01{1}}sqrt{1660/0.044(frac{0.01{1})}}

$$\frac{ 1 }{ 2 \cdot 165 \frac{ 0.01 }{ 1 } } \sqrt{ \frac{ 1660 }{ 0.044( \frac{ 0.01 }{ 1 } ) } }$$

Evaluate

$$\frac{25000\sqrt{1826}}{181511}\approx 5.885555316$$

Solution Steps

Multiply 165 and 1 to get 165.

$$\frac{1}{2\times \frac{165+0.01}{1}}\sqrt{\frac{1660}{0.044\times \frac{0.01}{1}}}$$

Add 165 and 0.01 to get 165.01.

$$\frac{1}{2\times \frac{165.01}{1}}\sqrt{\frac{1660}{0.044\times \frac{0.01}{1}}}$$

Anything divided by one gives itself.

$$\frac{1}{2\times 165.01}\sqrt{\frac{1660}{0.044\times \frac{0.01}{1}}}$$

Multiply 2 and 165.01 to get 330.02.

$$\frac{1}{330.02}\sqrt{\frac{1660}{0.044\times \frac{0.01}{1}}}$$

Expand \frac{1}{330.02} by multiplying both numerator and the denominator by 100.

$$\frac{100}{33002}\sqrt{\frac{1660}{0.044\times \frac{0.01}{1}}}$$

Reduce the fraction \frac{100}{33002} to lowest terms by extracting and canceling out 2.

$$\frac{50}{16501}\sqrt{\frac{1660}{0.044\times \frac{0.01}{1}}}$$

Anything divided by one gives itself.

$$\frac{50}{16501}\sqrt{\frac{1660}{0.044\times 0.01}}$$

Multiply 0.044 and 0.01 to get 0.00044.

$$\frac{50}{16501}\sqrt{\frac{1660}{0.00044}}$$

Expand \frac{1660}{0.00044} by multiplying both numerator and the denominator by 100000.

$$\frac{50}{16501}\sqrt{\frac{166000000}{44}}$$

Reduce the fraction \frac{166000000}{44} to lowest terms by extracting and canceling out 4.

$$\frac{50}{16501}\sqrt{\frac{41500000}{11}}$$

Rewrite the square root of the division \sqrt{\frac{41500000}{11}} as the division of square roots \frac{\sqrt{41500000}}{\sqrt{11}}.

$$\frac{50}{16501}\times \frac{\sqrt{41500000}}{\sqrt{11}}$$

Factor 41500000=500^{2}\times 166. Rewrite the square root of the product \sqrt{500^{2}\times 166} as the product of square roots \sqrt{500^{2}}\sqrt{166}. Take the square root of 500^{2}.

$$\frac{50}{16501}\times \frac{500\sqrt{166}}{\sqrt{11}}$$

Rationalize the denominator of \frac{500\sqrt{166}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{50}{16501}\times \frac{500\sqrt{166}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{50}{16501}\times \frac{500\sqrt{166}\sqrt{11}}{11}$$

To multiply \sqrt{166} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{50}{16501}\times \frac{500\sqrt{1826}}{11}$$

Multiply \frac{50}{16501} times \frac{500\sqrt{1826}}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50\times 500\sqrt{1826}}{16501\times 11}$$

Multiply 50 and 500 to get 25000.

$$\frac{25000\sqrt{1826}}{16501\times 11}$$

Multiply 16501 and 11 to get 181511.

$$\frac{25000\sqrt{1826}}{181511}$$