Solve sqrt{54}+2/sqrt{6}

$$\sqrt { 54 } + \frac { 2 } { \sqrt { 6 } }$$

Evaluate

$$\frac{10\sqrt{6}}{3}\approx 8.164965809$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\sqrt{6}+\frac{2}{\sqrt{6}}$$

Rationalize the denominator of \frac{2}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$3\sqrt{6}+\frac{2\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$3\sqrt{6}+\frac{2\sqrt{6}}{6}$$

Divide 2\sqrt{6} by 6 to get \frac{1}{3}\sqrt{6}.

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

Combine 3\sqrt{6} and \frac{1}{3}\sqrt{6} to get \frac{10}{3}\sqrt{6}.

$$\frac{10}{3}\sqrt{6}$$