Solve sqrt{200*14.8*200000/14.80*20%}

$$\sqrt{ \frac{ 200 \times 14.8 \times 200000 }{ 14.80 \times 20 \% } }$$

Evaluate

$$10000\sqrt{2}\approx 14142.135623731$$

Solution Steps

Multiply 200 and 14.8 to get 2960.

$$\sqrt{\frac{2960\times 200000}{14.8\times \frac{20}{100}}}$$

Multiply 2960 and 200000 to get 592000000.

$$\sqrt{\frac{592000000}{14.8\times \frac{20}{100}}}$$

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

$$\sqrt{\frac{592000000}{14.8\times \frac{1}{5}}}$$

Convert decimal number 14.8 to fraction \frac{148}{10}. Reduce the fraction \frac{148}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{592000000}{\frac{74}{5}\times \frac{1}{5}}}$$

Multiply \frac{74}{5} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{592000000}{\frac{74\times 1}{5\times 5}}}$$

Do the multiplications in the fraction \frac{74\times 1}{5\times 5}.

$$\sqrt{\frac{592000000}{\frac{74}{25}}}$$

Divide 592000000 by \frac{74}{25} by multiplying 592000000 by the reciprocal of \frac{74}{25}.

$$\sqrt{592000000\times \frac{25}{74}}$$

Express 592000000\times \frac{25}{74} as a single fraction.

$$\sqrt{\frac{592000000\times 25}{74}}$$

Multiply 592000000 and 25 to get 14800000000.

$$\sqrt{\frac{14800000000}{74}}$$

Divide 14800000000 by 74 to get 200000000.

$$\sqrt{200000000}$$

Factor 200000000=10000^{2}\times 2. Rewrite the square root of the product \sqrt{10000^{2}\times 2} as the product of square roots \sqrt{10000^{2}}\sqrt{2}. Take the square root of 10000^{2}.

$$10000\sqrt{2}$$