Question
Simplify six over square root of 3 plus 2
Answers
Answered by
GPT 3.5
To simplify the expression 6/(√3 + 2), we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
So, 6/(√3 + 2) = 6/(√3 + 2) * (√3 - 2)/(√3 - 2)
= 6(√3 - 2)/((√3)^2 - 2^2)
= 6(√3 - 2)/(3 - 4)
= 6(√3 - 2)/(-1)
= -6(√3 - 2)
Therefore, 6/(√3 + 2) simplifies to -6√3 + 12.
So, 6/(√3 + 2) = 6/(√3 + 2) * (√3 - 2)/(√3 - 2)
= 6(√3 - 2)/((√3)^2 - 2^2)
= 6(√3 - 2)/(3 - 4)
= 6(√3 - 2)/(-1)
= -6(√3 - 2)
Therefore, 6/(√3 + 2) simplifies to -6√3 + 12.