Rút gọn

To simplify the expression √(1- √3)^2 - √3, we can start by expanding the square of (1-√3):

(1-√3)^2 = (1-√3)(1-√3) = 1 - √3 - √3 + (√3)^2
= 1 - 2√3 + 3
= 4 - 2√3

Now, substituting this back into the original expression:

√(1- √3)^2 - √3 = √(4 - 2√3) - √3

Since the square root of a square is the absolute value of the number inside the square root, we have:

√(4 - 2√3) - √3 = |2 - √3| - √3

To simplify further, we can rationalize the denominator of the first term:

|2 - √3| - √3 = |2 - √3| - (√3 * (√3/√3))
= |2 - √3| - (√3^2/√3)
= |2 - √3| - 3/√3
= |2 - √3| - 3√3/3
= |2 - √3| - √3

So, the simplified expression is |2 - √3| - √3.