Solve (sqrt{48}+sqrt{3})divsqrt{27}

$$( \sqrt { 48 } + \sqrt { 3 } ) \div \sqrt { 27 }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

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}.

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

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

$$\frac{5\sqrt{3}}{\sqrt{27}}$$

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}.

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

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

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$