Solve frac{sqrt{27}+sqrt{75}}{sqrt{48}}

$$\frac { \sqrt { 27 } + \sqrt { 75 } } { \sqrt { 48 } }$$

Evaluate

$$2$$

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}.

$$\frac{3\sqrt{3}+\sqrt{75}}{\sqrt{48}}$$

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}.

$$\frac{3\sqrt{3}+5\sqrt{3}}{\sqrt{48}}$$

Combine 3\sqrt{3} and 5\sqrt{3} to get 8\sqrt{3}.

$$\frac{8\sqrt{3}}{\sqrt{48}}$$

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}.

$$\frac{8\sqrt{3}}{4\sqrt{3}}$$

Cancel out 4\sqrt{3} in both numerator and denominator.

$$2$$

Factor

$$2$$