Simplify the expression. (6)/(1+√(3) )

Question

Simplify the expression.


`(6)/(1+√(3) )`

Answer 1

Explanation:

Rationalize the denominator by multiplying both denominator & numerator by the conjugate of the denominator.

Conjugate of the denominator 1 + √3 is 1 - √3

`(6)/(1+√(3))=(6(1-√(3)))/((1+√(3))(1-√(3)))\\\\=(6(1-√(3)))/((1+√(3))(1-√(3)))\\\\=(6(1-√(3)))/(1^(2)-(√(3))^(2))\\\\=(6(1-√(3)))/(1-3)\\\\=(6(1-√(3)))/(-2)\\\\=(-3)(1-√(3))\\\\=-3+3√(3)`