Advanced MathHardSquaring a radical binomial
Advanced Math practice question
For x > 0, the expression (√x + 3)² can be written as x + a√x + 9. What is the value of a?
Answer: 6
(√x + 3)² = x + 2 · 3 · √x + 9 = x + 6√x + 9, so a = 6.
Common wrong answers
- If you answered 2
- 2 is only the doubling factor; multiply by the 3.
- If you answered 3
- The cross term doubles the product: 2 · 3 = 6.
- If you answered 9
- 9 is the constant 3²; the √x coefficient is 6.
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