We know that a and b are POSITIVE

There's a nice rule that says: if 0 < x < y, then 0 < x² < y²
In other words, if both quantities are POSITIVE then, if we square both quantities, the comparison remains the same.

So, let's square both quantities to get:
QUANTITY A: [√(a + b)]²
QUANTITY B: (√a + √b)²

Simplify:
QUANTITY A: a + b
QUANTITY B: (√a + √b)(√a + √b)

Apply FOIL to Quantity B:
QUANTITY A: a + b
QUANTITY B: a + √ab + √ab + b

Simplify:
QUANTITY A: a + b
QUANTITY B: a + 2√ab + b

Subtract a from both quantities:
QUANTITY A: b
QUANTITY B: 2√ab + b

Subtract b from both quantities:
QUANTITY A: 0
QUANTITY B: 2√ab

Since a and b are both POSITIVE, √ab must be POSITIVE, which means 2√ab must be POSITIVE
We get:
QUANTITY A: 0
QUANTITY B: some POSITIVE number

Answer: B

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