Solve sqrt{6*6.410^6/9.8}div3600

$$\sqrt{ \frac{ 6 \cdot 6.4 { 10 }^{ 6 } }{ 9.8 } } \div 3600$$

Evaluate

$$\frac{20\sqrt{3}}{63}\approx 0.549857399$$

Solution Steps

Multiply 6 and 6.4 to get 38.4.

$$\frac{\sqrt{\frac{38.4\times 10^{6}}{9.8}}}{3600}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\sqrt{\frac{38.4\times 1000000}{9.8}}}{3600}$$

Multiply 38.4 and 1000000 to get 38400000.

$$\frac{\sqrt{\frac{38400000}{9.8}}}{3600}$$

Expand \frac{38400000}{9.8} by multiplying both numerator and the denominator by 10.

$$\frac{\sqrt{\frac{384000000}{98}}}{3600}$$

Reduce the fraction \frac{384000000}{98} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{\frac{192000000}{49}}}{3600}$$

Rewrite the square root of the division \sqrt{\frac{192000000}{49}} as the division of square roots \frac{\sqrt{192000000}}{\sqrt{49}}.

$$\frac{\frac{\sqrt{192000000}}{\sqrt{49}}}{3600}$$

Factor 192000000=8000^{2}\times 3. Rewrite the square root of the product \sqrt{8000^{2}\times 3} as the product of square roots \sqrt{8000^{2}}\sqrt{3}. Take the square root of 8000^{2}.

$$\frac{\frac{8000\sqrt{3}}{\sqrt{49}}}{3600}$$

Calculate the square root of 49 and get 7.

$$\frac{\frac{8000\sqrt{3}}{7}}{3600}$$

Express \frac{\frac{8000\sqrt{3}}{7}}{3600} as a single fraction.

$$\frac{8000\sqrt{3}}{7\times 3600}$$

Cancel out 400 in both numerator and denominator.

$$\frac{20\sqrt{3}}{7\times 9}$$

Multiply 7 and 9 to get 63.

$$\frac{20\sqrt{3}}{63}$$