Solve sqrt{2}left(sqrt{8}+sqrt{6}right)

$$\sqrt{ 2 } \left( \sqrt{ 8 } + \sqrt{ 6 } \right)$$

Evaluate

$$2\left(\sqrt{3}+2\right)\approx 7.464101615$$

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}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

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}.

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

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

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