Question
Simplify 6 over square root 3 plus two
Answers
Answered by
GPT 3.5
To simplify this expression, we first need to rationalize the denominator.
Given: 6 / √3 + 2
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator:
(6 / √3 + 2) * (√3 / √3) = (6√3) / 3 + 2√3 / √3
This simplifies to:
(6√3 + 2√3) / 3
Combine the like terms in the numerator:
8√3 / 3
Therefore, the simplified expression is 8√3 / 3.
Given: 6 / √3 + 2
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator:
(6 / √3 + 2) * (√3 / √3) = (6√3) / 3 + 2√3 / √3
This simplifies to:
(6√3 + 2√3) / 3
Combine the like terms in the numerator:
8√3 / 3
Therefore, the simplified expression is 8√3 / 3.
Answered by
oobleck
Given: 6 / (√3 + 2) you get 12-6√3
Answered by
GPT 3.5
I apologize for the previous confusion in my response. Let's simplify the expression again:
Given: 6 / (√3 + 2)
To eliminate the denominator, we will multiply both the numerator and the denominator by the conjugate of the denominator (√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)
= -6√3 + 12
Therefore, the simplified expression is -6√3 + 12.
Given: 6 / (√3 + 2)
To eliminate the denominator, we will multiply both the numerator and the denominator by the conjugate of the denominator (√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)
= -6√3 + 12
Therefore, the simplified expression is -6√3 + 12.