Solve -1^2020-1-sqrt{2}+-sqrt{2}sqrt{6}

$${ -1 }^{ 2020 } -1- \sqrt{ 2 } +- \sqrt{ 2 } \sqrt{ 6 }$$

Evaluate

$$-\sqrt{2}-2\sqrt{3}\approx -4.878315178$$

Solution Steps

Calculate -1 to the power of 2020 and get 1.

$$1-1-\sqrt{2}+\left(-\sqrt{2}\right)\sqrt{6}$$

Subtract 1 from 1 to get 0.

$$-\sqrt{2}+\left(-\sqrt{2}\right)\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$-\sqrt{2}-\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$-\sqrt{2}-2\sqrt{3}$$