Question

How do you simplify `(5 + sqrt 3) /( 2 - sqrt3)`?

Answer 1

`(5+sqrt(3))/(2-sqrt(3))=13+7sqrt(3)`

Explanation:

Using `a^2-b^2=(a+b)(a-b)`

You can write the value 1 in many ways: `2/2; 16/16; or 1=(2+sqrt(3))/(2+sqrt(3))`

Multiply by 1 but in the form `1=(2+sqrt(3))/(2+sqrt(3))` giving

`(5+sqrt(3))/(2-sqrt(3)) xx (2+sqrt(3))/(2+sqrt(3))" "=" "( (5+sqrt(3))(2+sqrt(3)))/(2^2 -[(sqrt(3))^2])`

`=> (10+5sqrt(3)+2sqrt(3)+3)/(4-3)`

`=>13+7sqrt(3)`