Solve frac{sqrt{27}}{sqrt{48}}=

$$\frac { \sqrt { 27 } } { \sqrt { 48 } } =$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3\sqrt{3}}{\sqrt{48}}$$

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}.

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

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

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$