Solve sqrt{2*5000/9.80}

$$\sqrt{ \frac{ 2 \cdot 5000 }{ 9.80 } }$$

Evaluate

$$\frac{100\sqrt{5}}{7}\approx 31.94382825$$

Solution Steps

Multiply 2 and 5000 to get 10000.

$$\sqrt{\frac{10000}{9.8}}$$

Expand \frac{10000}{9.8} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{100000}{98}}$$

Reduce the fraction \frac{100000}{98} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{50000}{49}}$$

Rewrite the square root of the division \sqrt{\frac{50000}{49}} as the division of square roots \frac{\sqrt{50000}}{\sqrt{49}}.

$$\frac{\sqrt{50000}}{\sqrt{49}}$$

Factor 50000=100^{2}\times 5. Rewrite the square root of the product \sqrt{100^{2}\times 5} as the product of square roots \sqrt{100^{2}}\sqrt{5}. Take the square root of 100^{2}.

$$\frac{100\sqrt{5}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{100\sqrt{5}}{7}$$