Solve frac{sqrt{9.8*6.4*10^6}}{3.6}

$$\frac { \sqrt { 9.8 \times 6.4 \times 10 ^ { 6 } } } { 3.6 }$$

Evaluate

$$\frac{14000\sqrt{2}}{9}\approx 2199.887763691$$

Solution Steps

Multiply 9.8 and 6.4 to get 62.72.

$$\frac{\sqrt{62.72\times 10^{6}}}{3.6}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\sqrt{62.72\times 1000000}}{3.6}$$

Multiply 62.72 and 1000000 to get 62720000.

$$\frac{\sqrt{62720000}}{3.6}$$

Factor 62720000=5600^{2}\times 2. Rewrite the square root of the product \sqrt{5600^{2}\times 2} as the product of square roots \sqrt{5600^{2}}\sqrt{2}. Take the square root of 5600^{2}.

$$\frac{5600\sqrt{2}}{3.6}$$

Divide 5600\sqrt{2} by 3.6 to get \frac{14000}{9}\sqrt{2}.

$$\frac{14000}{9}\sqrt{2}$$