Advanced MathHardCombining radicals with the same radicand
Advanced Math practice question
For x > 0, the expression √(50x⁴) − √(8x⁴) can be written as kx²√2, where k is a constant. What is the value of k?
Answer: 3
√(50x⁴) = √25 · √2 · x² = 5x²√2, and √(8x⁴) = √4 · √2 · x² = 2x²√2. The difference is 3x²√2, so k = 3.
Common wrong answers
- If you answered 7
- 7 is 5 + 2, adding instead of subtracting.
- If you answered 10
- 10 is 5 × 2, multiplying the coefficients instead of subtracting them.
- If you answered 42
- 42 is 50 − 8, subtracting under the radicals, which is not allowed.
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