Question

What is the quotient of 1 over (1 plus the square root of 3)?

Answer 1

You can rationalize the denominator by multiplying by 1 in the form of the conjugate of the denominator divided by itself.


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

This eqvaluates to approximately 0.3660254037844386.