Solve 5sqrt{3}+2sqrt{27}+1/sqrt{3}

$$5 \sqrt { 3 } + 2 \sqrt { 27 } + \frac { 1 } { \sqrt { 3 } }$$

Evaluate

$$\frac{34\sqrt{3}}{3}\approx 19.629909152$$

Solution Steps

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}.

$$5\sqrt{3}+2\times 3\sqrt{3}+\frac{1}{\sqrt{3}}$$

Multiply 2 and 3 to get 6.

$$5\sqrt{3}+6\sqrt{3}+\frac{1}{\sqrt{3}}$$

Combine 5\sqrt{3} and 6\sqrt{3} to get 11\sqrt{3}.

$$11\sqrt{3}+\frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$11\sqrt{3}+\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$11\sqrt{3}+\frac{\sqrt{3}}{3}$$

Combine 11\sqrt{3} and \frac{\sqrt{3}}{3} to get \frac{34}{3}\sqrt{3}.

$$\frac{34}{3}\sqrt{3}$$