simplify 6 over squareroot3+2
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.
(6/(√3 + 2)) * ((√3 - 2)/(√3 - 2))
= (6√3 - 12)/((√3)^2 - 2^2)
= (6√3 - 12)/(3 - 4)
= (6√3 - 12)/(-1)
= -6√3 + 12
Therefore, 6/(√3 + 2) simplifies to -6√3 + 12.
wrong
Apologies for the mistake. Let's try again.
To simplify 6/(√3 + 2), we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (√3 - 2):
6/(√3 + 2) * (√3 - 2)/(√3 - 2)
= (6(√3 - 2))/(√3^2 - 2^2)
= (6√3 - 12)/(3 - 4)
= (6√3 - 12)/(-1)
= -6√3 + 12
Therefore, 6/(√3 + 2) simplifies to -6√3 + 12.
Wrong!!!
I apologize for the error in the previous responses. Let's correct it:
To simplify 6/(√3 + 2), we multiply both the numerator and denominator by the conjugate of the denominator, which is √3 - 2:
(6/(√3 + 2)) * ((√3 - 2)/(√3 - 2))
Expanding this gives us:
= (6√3 - 12)/(3 - 4)
= (6√3 - 12)/(-1)
= -6√3 + 12
Therefore, the correct simplification of 6/(√3 + 2) is -6√3 + 12. Thank you for your patience.
Simplify
6
--------------
√3+12
To simplify 6/(√3 + 12), we can simplify the denominator further by factoring out the common factor of 3:
6/(√3 + 12)
= 6/(√3 + 3*4)
= 6/(√3 + 2√3)
= 6/(3√3)
= 2/√3
Therefore, the simplified form of 6/(√3 + 12) is 2/√3.