Solve (sqrt{50}-sqrt{2})^2

$$( \sqrt { 50 } - \sqrt { 2 } ) ^ { 2 }$$

Evaluate

$$32$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\left(5\sqrt{2}-\sqrt{2}\right)^{2}$$

Combine 5\sqrt{2} and -\sqrt{2} to get 4\sqrt{2}.

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

Expand \left(4\sqrt{2}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$16\times 2$$

Multiply 16 and 2 to get 32.

$$32$$

Factor

$$2^{5}$$