Solve 10/6sqrt{12}+7/2sqrt{27}

$$\frac{ 10 }{ 6 } \sqrt{ 12 } + \frac{ 7 }{ 2 } \sqrt{ 27 }$$

Evaluate

$$\frac{83\sqrt{3}}{6}\approx 23.960036171$$

Solution Steps

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}\sqrt{12}+\frac{7}{2}\sqrt{27}$$

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}.

$$\frac{5}{3}\times 2\sqrt{3}+\frac{7}{2}\sqrt{27}$$

Express \frac{5}{3}\times 2 as a single fraction.

$$\frac{5\times 2}{3}\sqrt{3}+\frac{7}{2}\sqrt{27}$$

Multiply 5 and 2 to get 10.

$$\frac{10}{3}\sqrt{3}+\frac{7}{2}\sqrt{27}$$

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}.

$$\frac{10}{3}\sqrt{3}+\frac{7}{2}\times 3\sqrt{3}$$

Express \frac{7}{2}\times 3 as a single fraction.

$$\frac{10}{3}\sqrt{3}+\frac{7\times 3}{2}\sqrt{3}$$

Multiply 7 and 3 to get 21.

$$\frac{10}{3}\sqrt{3}+\frac{21}{2}\sqrt{3}$$

Combine \frac{10}{3}\sqrt{3} and \frac{21}{2}\sqrt{3} to get \frac{83}{6}\sqrt{3}.

$$\frac{83}{6}\sqrt{3}$$