Solve sqrt{2*50/9,8}

$$\sqrt { \frac { 2 \cdot 50 } { 9,8 } }$$

Evaluate

$$\frac{10\sqrt{5}}{7}\approx 3.194382825$$

Solution Steps

Multiply 2 and 50 to get 100.

$$\sqrt{\frac{100}{9,8}}$$

Expand \frac{100}{9,8} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1000}{98}}$$

Reduce the fraction \frac{1000}{98} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{500}{49}}$$

Rewrite the square root of the division \sqrt{\frac{500}{49}} as the division of square roots \frac{\sqrt{500}}{\sqrt{49}}.

$$\frac{\sqrt{500}}{\sqrt{49}}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$\frac{10\sqrt{5}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{10\sqrt{5}}{7}$$