Solve sqrt{3}*(sqrt{133}+2/sqrt{3})

$$\sqrt { 3 } \cdot ( \sqrt { 133 } + \frac { 2 } { \sqrt { 3 } } )$$

Evaluate

$$\sqrt{399}+2\approx 21.974984355$$

Short Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}\left(\sqrt{133}+\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)$$

The square of \sqrt{3} is 3.

$$\sqrt{3}\left(\sqrt{133}+\frac{2\sqrt{3}}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{133} times \frac{3}{3}.

$$\sqrt{3}\left(\frac{3\sqrt{133}}{3}+\frac{2\sqrt{3}}{3}\right)$$

Since \frac{3\sqrt{133}}{3} and \frac{2\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{3}\times \frac{3\sqrt{133}+2\sqrt{3}}{3}$$

Express \sqrt{3}\times \frac{3\sqrt{133}+2\sqrt{3}}{3} as a single fraction.

$$\frac{\sqrt{3}\left(3\sqrt{133}+2\sqrt{3}\right)}{3}$$

Use the distributive property to multiply \sqrt{3} by 3\sqrt{133}+2\sqrt{3}.

$$\frac{3\sqrt{3}\sqrt{133}+2\left(\sqrt{3}\right)^{2}}{3}$$

To multiply \sqrt{3} and \sqrt{133}, multiply the numbers under the square root.

$$\frac{3\sqrt{399}+2\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{3\sqrt{399}+2\times 3}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{3\sqrt{399}+6}{3}$$

Divide each term of 3\sqrt{399}+6 by 3 to get \sqrt{399}+2.

$$\sqrt{399}+2$$