Solve (sqrt{20}-sqrt{80})^2

$$( \sqrt { 20 } - \sqrt { 80 } ) ^ { 2 }$$

Evaluate

$$20$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\left(2\sqrt{5}-\sqrt{80}\right)^{2}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\left(2\sqrt{5}-4\sqrt{5}\right)^{2}$$

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

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

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

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

Calculate -2 to the power of 2 and get 4.

$$4\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$4\times 5$$

Multiply 4 and 5 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$