Advanced MathHardExpanding the square of a sum of surds
Advanced Math practice question
The expression (√5 + √2)² can be written as a + b√10, where a and b are integers. What is the value of a + b?
Answer: 9
(√5 + √2)² = 5 + 2√10 + 2 = 7 + 2√10. So a = 7, b = 2, and a + b = 9.
Common wrong answers
- If you answered 7
- 7 is a alone, forgetting the middle term.
- If you answered 8
- 8 comes from b = 1, forgetting to double the cross term.
- If you answered 17
- 17 comes from a = 7 and b = 10, mistaking the radicand for the coefficient.
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