AQA · Mathematics · 8300
GCSE Maths: Surds: addition/subtraction
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Surds: addition/subtraction (Corbettmaths Video 306), 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)
What is (√a)² equal to?
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a
What is √a ÷ √b equal to?
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√(a ÷ b) or √(a/b)
To simplify a surd like √50, look for the largest ? factor.
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perfect square
How do you simplify √50?
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5√2 (because √50 = √(25 × 2) = √25 × √2 = 5√2)
When adding or subtracting surds, what must the surds have in common?
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They must have the same surd part (like √2 + √2 or 3√5 + 2√5)
What does it mean to rationalise a denominator?
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To remove surds from the denominator of a fraction, typically by multiplying numerator and denominator by the surd.
What is the result of (a + √b)(a - √b)?
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a² - b (the surd terms cancel out)
When expanding (√a + √b)², you get a + 2√(ab) + ?
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b
What is (√3)³ equal to?
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3√3 (because (√3)³ = √3 × √3 × √3 = 3 × √3)
Express √32 in its simplest form.
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4√2
Why is it incorrect to simplify √2 + √8 as √10?
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You cannot add the numbers inside different square roots. First simplify each surd separately (√8 = 2√2), then combine like terms: √2 + 2√2 = 3√2.
Express √2 + √98 in the form a√2 where a is an integer.
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8√2. Since √98 = √(49×2) = 7√2, we have √2 + 7√2 = 8√2.
Write √150 + √24 in the form k√6.
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7√6. √150 = √(25×6) = 5√6 and √24 = √(4×6) = 2√6, so 5√6 + 2√6 = 7√6.
What is the perimeter of a rectangle with sides 5√2 cm and √2 cm?
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12√2 cm. Perimeter = 2(5√2 + √2) = 2(6√2) = 12√2 cm.
What is the area of a rectangle with sides 5√2 cm and √2 cm?
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10 cm². Area = 5√2 × √2 = 5 × 2 = 10 cm².
Simplify √6 × √8 and express in the form a√3.
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4√3. √6 × √8 = √48 = √(16×3) = 4√3.
Rationalise the denominator of 15/√5.
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3√5. Multiply numerator and denominator by √5: (15√5)/5 = 3√5.
Evaluate (5 + √2)(5 − √2).
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23. This is a difference of squares: (5)² − (√2)² = 25 − 2 = 23.
Simplify √3(√27 − √3).
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6. √3 × √27 = √81 = 9 and √3 × √3 = 3, so 9 − 3 = 6.
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