Asked by htht
Given that a equal sign with line going through it is it ever possible to have
squareroot a +squareroot b =sqaureroot a+b Explain.
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the symbol as the square-root for real numbers (so a,b ≥ 0). Square both sides:
(√a + √b)² = a + b + 2√(ab).
If √a + √b = √(a + b) then
a + b + 2√(ab) = a + b,
so 2√(ab) = 0, hence √(ab) = 0 and ab = 0.
Thus the equality holds exactly when at least one of a or b is 0 (for example a = 4, b = 0 gives 2 + 0 = 2). For positive a and b the left side is strictly larger than √(a + b).
(√a + √b)² = a + b + 2√(ab).
If √a + √b = √(a + b) then
a + b + 2√(ab) = a + b,
so 2√(ab) = 0, hence √(ab) = 0 and ab = 0.
Thus the equality holds exactly when at least one of a or b is 0 (for example a = 4, b = 0 gives 2 + 0 = 2). For positive a and b the left side is strictly larger than √(a + b).
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