Solve 1/2(165)(frac{0.01{1})}*sqrt{1660/0.004}

$$\frac{ 1 }{ 2(165)( \frac{ 0.01 }{ 1 } ) } \times \sqrt{ \frac{ 1660 }{ 0.004 } }$$

Evaluate

$$\frac{500\sqrt{166}}{33}\approx 195.213617072$$

Solution Steps

Multiply 2 and 165 to get 330.

$$\frac{1}{330\times \frac{0.01}{1}}\sqrt{\frac{1660}{0.004}}$$

Anything divided by one gives itself.

$$\frac{1}{330\times 0.01}\sqrt{\frac{1660}{0.004}}$$

Multiply 330 and 0.01 to get 3.3.

$$\frac{1}{3.3}\sqrt{\frac{1660}{0.004}}$$

Expand \frac{1}{3.3} by multiplying both numerator and the denominator by 10.

$$\frac{10}{33}\sqrt{\frac{1660}{0.004}}$$

Expand \frac{1660}{0.004} by multiplying both numerator and the denominator by 1000.

$$\frac{10}{33}\sqrt{\frac{1660000}{4}}$$

Divide 1660000 by 4 to get 415000.

$$\frac{10}{33}\sqrt{415000}$$

Factor 415000=50^{2}\times 166. Rewrite the square root of the product \sqrt{50^{2}\times 166} as the product of square roots \sqrt{50^{2}}\sqrt{166}. Take the square root of 50^{2}.

$$\frac{10}{33}\times 50\sqrt{166}$$

Express \frac{10}{33}\times 50 as a single fraction.

$$\frac{10\times 50}{33}\sqrt{166}$$

Multiply 10 and 50 to get 500.

$$\frac{500}{33}\sqrt{166}$$