my answer is B but the OA is A

Quick approach: Plug in values that makes under the root either of the root zero and other greater than or equal to zero X=2 satisfies both 1st adn 2 under root. Now solve question stem for x=2. on solving it we get zero and check answer choices that gives same value. Luckily there is only one. A

sana.noor wrote:If each expression under the square root is greater than or equal to 0, what is √(x^2 - 6x + 9) + √(2 - x) + x - 3? a. √(2-x) b. 2x - 6 + √(2-x) c. √(2-x) + x - 3 d. 2x - 6 + √(x-2) e. x + √(x-2) Here's the algebraic approach. √(x² - 6x + 9) + √(2 - x) + x - 3 = √[(x-3)(x-3)] + √(2 - x) + x - 3 = √(x-3)² + √(2 - x) + x - 3 IMPORTANT THING #1: all expressions under square root sign are greater than or equal to 0. Notice that we have the expression √(2 - x) If 2 - x > 0, then we know that x < 2 IMPORTANT THING #2: Notice that √k² = k or -k, depending on the value of k. If k = 5, then √k² = 5 (= k) If k = -5, then √k² = 5 (= -k) So, √k² = k or -k since the square root of a value must be greater than or equal to zero. Similarly, √(x-3)² = (x-3) or -(x-3) In other words, √(x-3)² = (x-3) or -x+3, depending on whether (x-3) is positive or negative. Since we already determined that x < 2, we can conclude that (x-3) is negative and (-x + 3) is positive. Since the square root of a value must be greater than or equal to zero it must be the case that √(x-3)² = -x + 3 Now back to our simplification... √(x-3)² + √(2 - x) + x - 3 = -x + 3 + √(2 - x) + x - 3 = √(2 - x) = A Cheers, Brent