Solve frac{sqrt{5}-6}{sqrt{3}}+sqrt{12}

$$\frac { \sqrt { 5 } - 6 } { \sqrt { 3 } } + \sqrt { 12 }$$

Evaluate

$$\frac{\sqrt{15}}{3}\approx 1.290994449$$

Short Solution Steps

Rationalize the denominator of \frac{\sqrt{5}-6}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(\sqrt{5}-6\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{12}$$

The square of \sqrt{3} is 3.

$$\frac{\left(\sqrt{5}-6\right)\sqrt{3}}{3}+\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{\left(\sqrt{5}-6\right)\sqrt{3}}{3}+2\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{3} times \frac{3}{3}.

$$\frac{\left(\sqrt{5}-6\right)\sqrt{3}}{3}+\frac{3\times 2\sqrt{3}}{3}$$

Since \frac{\left(\sqrt{5}-6\right)\sqrt{3}}{3} and \frac{3\times 2\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{\left(\sqrt{5}-6\right)\sqrt{3}+3\times 2\sqrt{3}}{3}$$

Do the multiplications in \left(\sqrt{5}-6\right)\sqrt{3}+3\times 2\sqrt{3}.

$$\frac{\sqrt{15}-6\sqrt{3}+6\sqrt{3}}{3}$$

Do the calculations in \sqrt{15}-6\sqrt{3}+6\sqrt{3}.

$$\frac{\sqrt{15}}{3}$$