Solve sqrt{12}+3/sqrt{2}*sqrt{6}

$$\sqrt { 12 } + \frac { 3 } { \sqrt { 2 } } \times \sqrt { 6 }$$

Evaluate

$$5\sqrt{3}\approx 8.660254038$$

Short Solution Steps

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}.

$$2\sqrt{3}+\frac{3}{\sqrt{2}}\sqrt{6}$$

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

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

The square of \sqrt{2} is 2.

$$2\sqrt{3}+\frac{3\sqrt{2}}{2}\sqrt{6}$$

Express \frac{3\sqrt{2}}{2}\sqrt{6} as a single fraction.

$$2\sqrt{3}+\frac{3\sqrt{2}\sqrt{6}}{2}$$

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

$$\frac{2\times 2\sqrt{3}}{2}+\frac{3\sqrt{2}\sqrt{6}}{2}$$

Since \frac{2\times 2\sqrt{3}}{2} and \frac{3\sqrt{2}\sqrt{6}}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\times 2\sqrt{3}+3\sqrt{2}\sqrt{6}}{2}$$

Do the multiplications in 2\times 2\sqrt{3}+3\sqrt{2}\sqrt{6}.

$$\frac{4\sqrt{3}+6\sqrt{3}}{2}$$

Do the calculations in 4\sqrt{3}+6\sqrt{3}.

$$\frac{10\sqrt{3}}{2}$$

Divide 10\sqrt{3} by 2 to get 5\sqrt{3}.

$$5\sqrt{3}$$