1,043 prompts matching "Structured question: simplifying a surd raised to a fractional index"
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Common Mistakes: Writing down the roots once the brackets are found
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Worked Example: Halving the coefficient of x and squaring it
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Quiz: Completing the square on x squared plus 6x
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Practice: Working through a quadratic by completing the square, step by step
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Spot My Mistake: Completing the square when the roots are not real
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Common Mistakes: Checking a completed square by expanding it again
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Final Revision: Why completing the square always works
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Learn: Deriving the quadratic formula by completing the square
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Quiz: A negative value of b in the quadratic formula
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Spot My Mistake: What the formula gives when the discriminant is nought
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Final Revision: A word problem solved with the quadratic formula
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Learn: The sum of the roots as minus b over a
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Worked Example: The product of the roots as c over a
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Quiz: Finding the sum and the product without solving the equation
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Practice: Forming an equation from a given sum and product
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Explain Back: Finding a missing coefficient from a stated sum of roots
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Spot My Mistake: Finding a missing coefficient from a stated product of roots
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Common Mistakes: Roots that are reciprocals of one another
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Final Revision: One root twice the other, and what that gives
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Learn: What makes an expression in the roots symmetric
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