Solve (sqrt{6}+sqrt{8})sqrt{3}

$$( \sqrt { 6 } + \sqrt { 8 } ) \sqrt { 3 }$$

Evaluate

$$\sqrt{2}\left(2\sqrt{3}+3\right)\approx 9.141620173$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

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}.

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

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

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

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

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