Solve frac{sqrt{98}}{sqrt{32}}

$$\frac { \sqrt { 98 } } { \sqrt { 32 } }$$

Evaluate

$$\frac{7}{4}=1.75$$

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}.

$$\frac{7\sqrt{2}}{\sqrt{32}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{7\sqrt{2}}{4\sqrt{2}}$$

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

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$