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Using (sqrt x + sqrt y)² = x + y + 2 sqrt(xy), express sqrt(7 + 2 sqrt10) in the form sqrt a + sqrt b with a <= b, and find b - a.

1. 3
2. 4
3. 0
4. 2

Correct answer: 3

Solution

We need a + b = 7 and ab = 10, giving a = 2, b = 5. Then sqrt(7 + 2 sqrt10) = sqrt2 + sqrt5, with a <= b meaning a = 2, b = 5, so b - a = 3.

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