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studyAlgebra
CoreMaths revision

Surds

Keep irrational quantities exact through simplification, operations and rationalisation.

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Focus points
✓Simplify square-root expressions.
✓Combine like surds.
✓Rationalise denominators.
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The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · simplifying surds
Simplify √72.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · combining surds
Simplify 3√12 − √27.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · surds and identities
Expand (√5+2)(√5−2).
Question 4FluencyCore
Original practice · Free Online Revision
Skill · rationalising
Rationalise 5/√3.
Question 5FluencyCore
Original practice · Free Online Revision
Skill · conjugates
Rationalise 3/(2+√5).
Question 6FluencyCore
Original practice · Free Online Revision
Skill · surds multiplication
Simplify (√18)(√8).
Question 7ReasoningCore
Original practice · Free Online Revision
Skill · exact reasoning
Show that √12 + √27 = 5√3.
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · conjugate reciprocal
If x=2+√3, find 1/x exactly.