Question

Can someone help me simplify? I need help

Answer 1

13+7√3

Explanation:

The denominator will be rational when it is multiplied by the opposite ± expression, called the conjugate.

`(5 + √(3))/(2-√(3))`

`= \frac{5 + √(3)} {2-√(3)} X (2+√(3))/(2+√(3))` Multiplying by 1 does not change the number. (It equals 1 because the numerator and denominator are the same).

`= \frac{(5 + √(3))(2+√(3))} {(2-√(3))(2+√(3))}}`

`= (10 + 5√(3) + 2√(3)+3 )/(4 - 2√(3)+ 2√(3)-3)` Distribute over brackets

`= (13 + 7√(3) )/(4 -3)` Combine like terms

`= (13 + 7√(3) )/(1)`

`= 13 + 7√(3)`