Solve (2+sqrt{3})2020*(2-sqrt{3})2022

$$(2+ \sqrt{ 3 } )2020 \times (2- \sqrt{ 3 } )2022$$

Evaluate

$$4084440$$

Solution Steps

Multiply 2020 and 2022 to get 4084440.

$$4084440\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)$$

Use the distributive property to multiply 4084440 by 2+\sqrt{3}.

$$\left(8168880+4084440\sqrt{3}\right)\left(2-\sqrt{3}\right)$$

Apply the distributive property by multiplying each term of 8168880+4084440\sqrt{3} by each term of 2-\sqrt{3}.

$$16337760-8168880\sqrt{3}+8168880\sqrt{3}-4084440\left(\sqrt{3}\right)^{2}$$

Combine -8168880\sqrt{3} and 8168880\sqrt{3} to get 0.

$$16337760-4084440\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16337760-4084440\times 3$$

Multiply -4084440 and 3 to get -12253320.

$$16337760-12253320$$

Subtract 12253320 from 16337760 to get 4084440.

$$4084440$$

Factor

$$2^{3}\times 3\times 5\times 101\times 337$$