728 prompts matching "simplifying an expression with fractional indices"
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Worked Example: Adding two surds that simplify to the same root
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Practice: Multiplying a whole number by a surd
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Worked Example: Rationalising a denominator that is a single surd
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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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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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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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Practice: A binary operation set out as a table
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Show All Working: Evaluating a repeated operation such as a*(b*c)
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Common Mistakes: A binary operation that is ordinary addition in disguise
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Worked Example: Testing the even numbers for closure under addition
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Practice: Testing a set for closure under multiplication
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Show All Working: Showing a set is not closed by a single counter-example
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Common Mistakes: Closure on a set of three elements under a stated rule
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Worked Example: Testing a*b against b*a for a given rule
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Worked Example: Testing whether star distributes over plus
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