Solve (sqrt{3}+2sqrt{3}+5sqrt{11})divsqrt{3}

$$( \sqrt { 3 } + 2 \sqrt { 3 } + 5 \sqrt { 11 } ) \div \sqrt { 3 }$$

Evaluate

$$\frac{5\sqrt{33}}{3}+3\approx 12.574271078$$

Solution Steps

Combine \sqrt{3} and 2\sqrt{3} to get 3\sqrt{3}.

$$\frac{3\sqrt{3}+5\sqrt{11}}{\sqrt{3}}$$

Rationalize the denominator of \frac{3\sqrt{3}+5\sqrt{11}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(3\sqrt{3}+5\sqrt{11}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(3\sqrt{3}+5\sqrt{11}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 3\sqrt{3}+5\sqrt{11} by \sqrt{3}.

$$\frac{3\left(\sqrt{3}\right)^{2}+5\sqrt{11}\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{3\times 3+5\sqrt{11}\sqrt{3}}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{9+5\sqrt{11}\sqrt{3}}{3}$$

To multiply \sqrt{11} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{9+5\sqrt{33}}{3}$$