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ScanSolve AI Answer
let's solve this one. Q.5. sqrt(2 + 2 + 2 4) First, let's recall the note from the previous questions: 180^ < < 270^. This means is in the third quadrant. Step 1: Simplify the innermost square root, sqrt(2 + 2 4). Factor out 2 from the expression under the square root: sqrt(2(1 + 4)) Use the double angle identity 1 + 2A = 2 ^2 A. Here, 2A = 4, so A = 2. sqrt(2(2 ^2 2)) = sqrt(4 ^2 2) Take the square root: |2 2| Step 2: Determine the sign of 2. Given 180^ < < 270^, multiplying by 2 gives 360^ < 2 < 540^. In this range, 2 can be positive or negative. For problems of this type, it is generally assumed that the terms simplify positively to continue the pattern. Thus, we assume 2 0, which means |2 2| = 2 2. Substitute this back into the main expression: sqrt(2 + 2 2) Step 3: Simplify the remaining expression, sqrt(2 + 2 2). Factor out 2: sqrt(2(1 + 2)) Use the double angle identity 1 + 2A = 2 ^2 A. Here, A = . sqrt(2(2 ^2 )) = sqrt(4 ^2 ) Take the square root: |2 | Step 4: Determine the sign of . From the given note, 180^ < < 270^. This means is in the third quadrant. In the third quadrant, the cosine function is negative. Therefore, |2 | = -2 . The final simplified expression is -2 . What's next? Send 'em!