Solve frac{sqrt{3}+sqrt{3}+sqrt{3}+sqrt{3}}{sqrt{3}}

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

Evaluate

$$4$$

Solution Steps

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

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

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

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

Combine 3\sqrt{3} and \sqrt{3} to get 4\sqrt{3}.

$$\frac{4\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{4\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{4\times 3}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$4$$

Factor

$$2^{2}$$