Solve sqrt{2000*2000-(2828div2)*(2828div2)}

$$\sqrt{ 2000 \times 2000-(2828 \div 2) \times (2828 \div 2) }$$

Evaluate

$$2\sqrt{500151}\approx 1414.427092501$$

Solution Steps

Multiply \frac{2828}{2} and \frac{2828}{2} to get \left(\frac{2828}{2}\right)^{2}.

$$\sqrt{2000\times 2000-\left(\frac{2828}{2}\right)^{2}}$$

Multiply 2000 and 2000 to get 4000000.

$$\sqrt{4000000-\left(\frac{2828}{2}\right)^{2}}$$

Divide 2828 by 2 to get 1414.

$$\sqrt{4000000-1414^{2}}$$

Calculate 1414 to the power of 2 and get 1999396.

$$\sqrt{4000000-1999396}$$

Subtract 1999396 from 4000000 to get 2000604.

$$\sqrt{2000604}$$

Factor 2000604=2^{2}\times 500151. Rewrite the square root of the product \sqrt{2^{2}\times 500151} as the product of square roots \sqrt{2^{2}}\sqrt{500151}. Take the square root of 2^{2}.

$$2\sqrt{500151}$$