Solve (2sqrt{2}+sqrt{3})*sqrt{6}

$$( 2 \sqrt { 2 } + \sqrt { 3 } ) \times \sqrt { 6 }$$

Evaluate

$$\sqrt{3}\left(\sqrt{6}+4\right)\approx 11.170843917$$

Solution Steps

Use the distributive property to multiply 2\sqrt{2}+\sqrt{3} by \sqrt{6}.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 2 to get 4.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

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

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