Solve frac{sqrt{48}}{3}+frac{sqrt{27}}{7}

$$\frac { \sqrt { 48 } } { 3 } + \frac { \sqrt { 27 } } { 7 }$$

Evaluate

$$\frac{37\sqrt{3}}{21}\approx 3.051708566$$

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}.

$$\frac{4\sqrt{3}}{3}+\frac{\sqrt{27}}{7}$$

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}.

$$\frac{4\sqrt{3}}{3}+\frac{3\sqrt{3}}{7}$$

Combine \frac{4\sqrt{3}}{3} and \frac{3\sqrt{3}}{7} to get \frac{37}{21}\sqrt{3}.

$$\frac{37}{21}\sqrt{3}$$