Solve frac{sqrt{48}+sqrt{75}}{sqrt{12}}

$$\frac { \sqrt { 48 } + \sqrt { 75 } } { \sqrt { 12 } }$$

Evaluate

$$\frac{9}{2}=4.5$$

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}.

$$\frac{4\sqrt{3}+\sqrt{75}}{\sqrt{12}}$$

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}.

$$\frac{4\sqrt{3}+5\sqrt{3}}{\sqrt{12}}$$

Combine 4\sqrt{3} and 5\sqrt{3} to get 9\sqrt{3}.

$$\frac{9\sqrt{3}}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{9\sqrt{3}}{2\sqrt{3}}$$

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

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$