Solve frac{sqrt{2*1800*200}}{8}

$$\frac { \sqrt { 2 \times 1800 \times 200 } } { 8 }$$

Evaluate

$$75\sqrt{2}\approx 106.066017178$$

Solution Steps

Multiply 2 and 1800 to get 3600.

$$\frac{\sqrt{3600\times 200}}{8}$$

Multiply 3600 and 200 to get 720000.

$$\frac{\sqrt{720000}}{8}$$

Factor 720000=600^{2}\times 2. Rewrite the square root of the product \sqrt{600^{2}\times 2} as the product of square roots \sqrt{600^{2}}\sqrt{2}. Take the square root of 600^{2}.

$$\frac{600\sqrt{2}}{8}$$

Divide 600\sqrt{2} by 8 to get 75\sqrt{2}.

$$75\sqrt{2}$$