Solve sqrt{2}(sqrt{24}+sqrt{8})

$$\sqrt { 2 } ( \sqrt { 24 } + \sqrt { 8 } )$$

Evaluate

$$4\left(\sqrt{3}+1\right)\approx 10.92820323$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

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}.

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

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

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

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}.

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

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

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}+2\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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