Solve frac{3sqrt{75}+sqrt{27}}{3}

$$\frac { 3 \sqrt { 75 } + \sqrt { 27 } } { 3 }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

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}.

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

Multiply 3 and 5 to get 15.

$$\frac{15\sqrt{3}+\sqrt{27}}{3}$$

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}.

$$\frac{15\sqrt{3}+3\sqrt{3}}{3}$$

Combine 15\sqrt{3} and 3\sqrt{3} to get 18\sqrt{3}.

$$\frac{18\sqrt{3}}{3}$$

Divide 18\sqrt{3} by 3 to get 6\sqrt{3}.

$$6\sqrt{3}$$