755 prompts matching "Expanding a bracket with a coefficient on x"
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Worked Example: Why the square root of a non-square whole number is irrational
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Practice: Deciding whether root 16 is rational or irrational
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Explain Back: Where the surds sit on the number line
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Show All Working: Classifying a mixed list of numbers as rational or irrational
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Common Mistakes: Why a rational number added to an irrational one stays irrational
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Practice: Collecting similar surds in an expression
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Common Mistakes: Expressing root 50 as a multiple of root 2
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Worked Example: Rationalising a denominator that is a single surd
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Explain Back: Simplifying the answer once the denominator is rational
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Show All Working: Checking a rationalised answer by decimal approximation
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Common Mistakes: Rationalising a denominator of the form root a over root b
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Worked Example: Why multiplying by the conjugate clears the surd
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Practice: Rationalising a denominator of the form a plus root b over c minus root d
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Explain Back: The difference of two squares applied to surd conjugates
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Show All Working: A conjugate where the surd term comes first
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Common Mistakes: Rationalising when both terms of the denominator are surds
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Worked Example: Squaring both sides safely when solving a surd equation
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Explain Back: Solving an equation where the surd must be isolated first
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Common Mistakes: A surd equation that has no real solution
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Worked Example: Reading the symbol used for a binary operation
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