AQA · Mathematics · 8300
GCSE Maths: Surds: rationalising denominators
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Surds: rationalising denominators (Corbettmaths Video 307), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is √a × √b equal to?
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√(a × b). The product of two surds equals the square root of the product of their radicands.
What is (√a)² equal to?
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a. Squaring a square root returns the original number under the root.
What is √a ÷ √b equal to?
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√(a ÷ b) or √a / √b. Division of surds equals the square root of the quotient.
How do you simplify √(a²b) where a is a perfect square factor?
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a√b. Extract the square root of the perfect square factor outside the radical.
What does 'rationalising the denominator' mean?
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Rewriting a fraction to eliminate surds from the denominator, typically by multiplying both numerator and denominator by an appropriate surd.
How do you rationalise a denominator of the form 1/√a?
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Multiply both numerator and denominator by √a to get √a/a.
How do you rationalise a denominator of the form 1/(a + √b)?
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Multiply both numerator and denominator by the conjugate (a - √b). This uses the difference of squares pattern.
What is the result of (a + √b)(a - √b)?
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a² - b. This is a difference of squares, used to eliminate surds when rationalising denominators.
To combine like surds such as 3√2 + 5√2, treat the surd as a ? and add the coefficients.
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variable
What is √8 simplified?
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2√2. Because √8 = √(4×2) = √4 × √2 = 2√2.
When expanding (√a + √b)², what is the result?
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a + 2√(ab) + b. Use FOIL or (x+y)² = x² + 2xy + y².
Is √2 + √8 equal to √10?
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No. √8 simplifies to 2√2, so √2 + √8 = √2 + 2√2 = 3√2, not √10.
Write √150 + √24 in the form k√6.
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7√6. (√150 = 5√6 and √24 = 2√6, so 5√6 + 2√6 = 7√6.)
What is the value of (5 + √2)(5 − √2)?
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23. (Using the difference of squares: 5² − (√2)² = 25 − 2 = 23.)
Simplify fully √3(√27 − √3).
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6. (√3 × √27 = √81 = 9; √3 × √3 = 3; so 9 − 3 = 6.)
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