AQA · Mathematics · 8300
GCSE Maths: Surds: intro, rules, simplifying
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Surds: intro, rules, simplifying (Corbettmaths Video 305), 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.
19 flashcards · Free to study · No account needed
Study this deck
Preparing your cards…
All questions and answers
Read through the full deck, or practise recalling each answer above.
What is the result of multiplying two surds: √a × √b?
Show answer
√(a × b). For example, √3 × √5 = √15.
What is the value of (√a)²?
Show answer
a. The square and square root cancel out. For example, (√5)² = 5.
How do you divide two surds: √a ÷ √b?
Show answer
√(a ÷ b) or √a/√b = √(a/b). For example, √21 ÷ √7 = √3.
How do you simplify a surd like √48?
Show answer
Factor out the largest perfect square: √48 = √(16 × 3) = √16 × √3 = 4√3.
When can you add or subtract surds?
Show answer
Only when they have the same surd part (like terms). For example, 2√3 + 5√3 = 7√3, but √2 + √3 cannot be simplified further.
To expand √a(b + √c), use the ? to multiply √a by each term inside the brackets.
Show answer
distributive property
What is the result of expanding (a + √b)(a − √b)?
Show answer
a² − b. This is a difference of squares. For example, (5 + √3)(5 − √3) = 25 − 3 = 22.
How do you rationalize a denominator of the form 1/√a?
Show answer
Multiply both numerator and denominator by √a. This gives √a/a.
What is the value of (√a)³?
Show answer
a√a or a^(3/2). For example, (√2)³ = 2√2.
What is √75 in its simplest form?
Show answer
5√3
What is √32 in its simplest form?
Show answer
4√2
What is √200 in its simplest form?
Show answer
10√2
Why is √2 + √8 NOT equal to √10?
Show answer
You cannot add the numbers under different square roots directly. Instead, simplify each surd first: √8 = 2√2, so √2 + √8 = √2 + 2√2 = 3√2.
Simplify √2 + √98 and express in the form a√2 where a is an integer.
Show answer
8√2 (since √98 = 7√2, so √2 + 7√2 = 8√2)
Simplify √6 × √8 and express in the form a√3.
Show answer
4√3. Since √6 × √8 = √48 = √(16 × 3) = 4√3.
Evaluate (5 + √2)(5 − √2).
Show answer
23. Using the difference of squares: (5 + √2)(5 − √2) = 5² − (√2)² = 25 − 2 = 23.
Simplify √3(√27 − √3).
Show answer
6. Since √3 × √27 = √81 = 9, and √3 × √3 = 3, so 9 − 3 = 6.
Express √11 + √99 in the form a√b where a and b are integers.
Show answer
4√11. Since √99 = √(9 × 11) = 3√11, so √11 + 3√11 = 4√11.
Simplify √80 − 10/√5.
Show answer
2√5. Since √80 = 4√5 and 10/√5 = 2√5 (rationalised), so 4√5 − 2√5 = 2√5.
Want to create your own cards? Create a free account. AI generation uses credits.