Solve sqrt[3]{27}+sqrt{2}(sqrt{2}+sqrt{8})

$$\sqrt[ 3 ] { 27 } + \sqrt { 2 } ( \sqrt { 2 } + \sqrt { 8 } )$$

Evaluate

$$9$$

Solution Steps

Calculate \sqrt[3]{27} and get 3.

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

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}.

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

Combine \sqrt{2} and 2\sqrt{2} to get 3\sqrt{2}.

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

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

$$3+2\times 3$$

Multiply 2 and 3 to get 6.

$$3+6$$

Add 3 and 6 to get 9.

$$9$$

Factor

$$3^{2}$$