Solve sqrt{200*148*200000/1480*20%}

$$\sqrt{ \frac{ 200 \times 148 \times 200000 }{ 1480 \times 20 \% } }$$

Evaluate

$$2000\sqrt{5}\approx 4472.135955$$

Solution Steps

Multiply 200 and 148 to get 29600.

$$\sqrt{\frac{29600\times 200000}{1480\times \frac{20}{100}}}$$

Multiply 29600 and 200000 to get 5920000000.

$$\sqrt{\frac{5920000000}{1480\times \frac{20}{100}}}$$

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$\sqrt{\frac{5920000000}{1480\times \frac{1}{5}}}$$

Multiply 1480 and \frac{1}{5} to get \frac{1480}{5}.

$$\sqrt{\frac{5920000000}{\frac{1480}{5}}}$$

Divide 1480 by 5 to get 296.

$$\sqrt{\frac{5920000000}{296}}$$

Divide 5920000000 by 296 to get 20000000.

$$\sqrt{20000000}$$

Factor 20000000=2000^{2}\times 5. Rewrite the square root of the product \sqrt{2000^{2}\times 5} as the product of square roots \sqrt{2000^{2}}\sqrt{5}. Take the square root of 2000^{2}.

$$2000\sqrt{5}$$