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

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

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}.

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

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

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

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}.

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

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

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

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

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