Question

7. Simplify. (Image: start-fraction 6 over start root 3 end root plus 2 end-fraction) (1 point)
(Image: Start Fraction 4 over Start Root 3 End Root End Fraction)
(Image: 12 minus 6 Start Root 3 End Root)
(Image: Start Root 3 End Root minus 2)
3

Answer 1

7. Simplify. 6/√3 +2 (1 point)
4/√3
12-6√3
√3 -2
3

Answer 2

(Type "3" in the answer box)

Start by rationalizing the denominator of the first expression by multiplying both the numerator and denominator by the conjugate of the denominator: Start fraction 6 over Start root 3 end root plus 2 end fraction times Start fraction Start root 3 end root minus 2 over Start fraction Start root 3 end root minus 2 end fraction. This simplifies to (6√3-12)/(3-4) = -6(√3-2)/(-1) = 6(√3-2). Therefore, the simplified expression is Start fraction 4 over Start root 3 end root = 4/√3. To simplify the third expression, multiply by the conjugate: Start root 3 end root minus 2 times Start root 3 end root + 2 over Start root 3 end root + 2. This simplifies to (3-4)=-1. Therefore, the simplified expression is -1. Out of the given answer choices, only 3 matches this result.

Answer 3

First, rationalize the denominator by multiplying both the numerator and denominator by √3 - 2:

(6/√3 + 2) * (√3 - 2)/(√3 - 2)

Simplifying this gives:

(6√3 - 12)/(3 - 4)

= -6(√3 - 2)/1

= -6√3 + 12

Out of the given answer choices, the closest equivalent is 12 - 6√3.