Solve frac{sqrt{48}}{sqrt{75}}

$$\frac { \sqrt { 48 } } { \sqrt { 75 } }$$

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{4\sqrt{3}}{\sqrt{75}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{4\sqrt{3}}{5\sqrt{3}}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$