Solve sqrt{2}(sqrt{12}+sqrt{8})

$$\sqrt{ 2 } ( \sqrt{ 12 } + \sqrt{ 8 } )$$

Evaluate

$$2\left(\sqrt{6}+2\right)\approx 8.898979486$$

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}.

$$\sqrt{2}\left(2\sqrt{3}+\sqrt{8}\right)$$

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}.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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