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

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

Evaluate

$$\frac{5600\sqrt{5}}{3}\approx 4173.993558$$

Solution Steps

Multiply 9.8 and 6.4 to get 62.72.

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

Calculate 10 to the power of 6 and get 1000000.

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

Multiply 62.72 and 1000000 to get 62720000.

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

Expand \frac{62720000}{3.6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{627200000}{36}}$$

Reduce the fraction \frac{627200000}{36} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{156800000}{9}}$$

Rewrite the square root of the division \sqrt{\frac{156800000}{9}} as the division of square roots \frac{\sqrt{156800000}}{\sqrt{9}}.

$$\frac{\sqrt{156800000}}{\sqrt{9}}$$

Factor 156800000=5600^{2}\times 5. Rewrite the square root of the product \sqrt{5600^{2}\times 5} as the product of square roots \sqrt{5600^{2}}\sqrt{5}. Take the square root of 5600^{2}.

$$\frac{5600\sqrt{5}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{5600\sqrt{5}}{3}$$