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

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

Evaluate

$$18$$

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}.

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

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

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

Expand \left(3\sqrt{2}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$9\times 2$$

Multiply 9 and 2 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$