Solve sqrt{12}*(sqrt{3}+sqrt{2}

$$\sqrt{ 12 } \times ( \sqrt{ 3 } + \sqrt{ 2 }$$

Evaluate

$$2\left(\sqrt{6}+3\right)\approx 10.898979486$$

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}.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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