Solve sqrt{20/2(9.8)}

$$\sqrt{ \frac{ 20 }{ 2(9.8) } }$$

Evaluate

$$\frac{5\sqrt{2}}{7}\approx 1.010152545$$

Solution Steps

Multiply 2 and 9.8 to get 19.6.

$$\sqrt{\frac{20}{19.6}}$$

Expand \frac{20}{19.6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{200}{196}}$$

Reduce the fraction \frac{200}{196} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{50}{49}}$$

Rewrite the square root of the division \sqrt{\frac{50}{49}} as the division of square roots \frac{\sqrt{50}}{\sqrt{49}}.

$$\frac{\sqrt{50}}{\sqrt{49}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{5\sqrt{2}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{5\sqrt{2}}{7}$$