Solve (3sqrt{2}-sqrt{8})^2

$$( 3 \sqrt { 2 } - \sqrt { 8 } ) ^ { 2 }$$

Evaluate

$$2$$

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}.

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

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

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

The square of \sqrt{2} is 2.

$$2$$

Factor

$$2$$