simplify: square root (4/3)-square root (3/4)

A. 2-sqaure root(3)/2 square root (3)
B. square root (7/12)
C. square root (3)/6
D. 2/square root (3)

which answer?

this is what i got square root (16/12)- square root (9/12)= square root (7/12)

√4/3 - √3/4 = √16/12 - √9/12 = √?

To simplify the expression √(4/3) - √(3/4), you need to follow these steps:

Step 1: Simplify the individual square roots within the expression.
√(4/3) = √4/√3 = 2/√3
√(3/4) = √3/√4 = √3/2

Step 2: Subtract the simplified square roots:
(2/√3) - (√3/2)

To rationalize the denominator, you need to multiply both the numerator and denominator of the first term by the conjugate of the denominator, which is √3. This will eliminate the square root in the denominator:

[(2/√3) * (√3/√3)] - (√3/2)
= (2√3/3) - (√3/2)

Now, to combine the terms, you need a common denominator, which is 6:
= (4√3/6) - (3√3/6)
= (4√3 - 3√3)/6
= √3/6

Therefore, the simplified expression is √3/6.

The correct answer is C.