√x² = |x|
|x| = x x>=0
= -x x < 0
---------
√(31 + 12√3) = √(4 + 2*2*3√3 + 27) = √(2² + 2*2*√27 + 27) = √(2 + √27)² = 2 + √27 = 2 + 3√3
√(9 - 4√5) = √(5 - 2*2*√5 + 4) = √(√5 - 2)² = {√5 - 2 > 0}=√5 - 2
√(13 - 4√3) = √(12 - 2*√12 + 1) = √(√12 - 1)² = (√12 - 1>0) =√12 - 1 = 2√3 - 1
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Verified answer
√x² = |x|
|x| = x x>=0
= -x x < 0
---------
√(31 + 12√3) = √(4 + 2*2*3√3 + 27) = √(2² + 2*2*√27 + 27) = √(2 + √27)² = 2 + √27 = 2 + 3√3
√(9 - 4√5) = √(5 - 2*2*√5 + 4) = √(√5 - 2)² = {√5 - 2 > 0}=√5 - 2
√(13 - 4√3) = √(12 - 2*√12 + 1) = √(√12 - 1)² = (√12 - 1>0) =√12 - 1 = 2√3 - 1
когда два ответа, то сразу