Solve sqrt{1/3}+sqrt{27}*sqrt{9}

$$\sqrt { \frac { 1 } { 3 } } + \sqrt { 27 } \times \sqrt { 9 }$$

Evaluate

$$\frac{28\sqrt{3}}{3}\approx 16.165807537$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\sqrt{1}}{\sqrt{3}}+\sqrt{27}\sqrt{9}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}+\sqrt{27}\sqrt{9}$$

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

$$\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{27}\sqrt{9}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{3}+\sqrt{27}\sqrt{9}$$

Factor 27=9\times 3. Rewrite the square root of the product \sqrt{9\times 3} as the product of square roots \sqrt{9}\sqrt{3}.

$$\frac{\sqrt{3}}{3}+\sqrt{9}\sqrt{3}\sqrt{9}$$

Multiply \sqrt{9} and \sqrt{9} to get 9.

$$\frac{\sqrt{3}}{3}+9\sqrt{3}$$

Combine \frac{\sqrt{3}}{3} and 9\sqrt{3} to get \frac{28}{3}\sqrt{3}.

$$\frac{28}{3}\sqrt{3}$$