Solve frac{sqrt{98}}{sqrt{200}}

$$\frac { \sqrt { 98 } } { \sqrt { 200 } }$$

Evaluate

$$\frac{7}{10}=0.7$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{7\sqrt{2}}{\sqrt{200}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{7\sqrt{2}}{10\sqrt{2}}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{7}{10}$$

Factor

$$\frac{7}{2 \cdot 5} = 0.7$$