lesson
Change the form without changing the value
1 · Learn
Multiplying numerator and denominator by the same non-zero quantity multiplies a fraction by one. This can remove a square root from a denominator. For 1/√2, multiply both by √2 to obtain √2/2.
For a two-term denominator, its conjugate may use the difference-of-squares identity. Preserve restrictions and do not multiply only the denominator.
2 · Worked example
3/√5 = 3√5/5. Both forms are exact and equivalent.
3 · Your turn
Rationalise 2/√3.
Check your answer
2√3/3.
4 · Apply your learning
Verify equivalence numerically without replacing the exact final answer by a rounded decimal.
Adult guidance and safety
This sequence includes extension mathematics and assumes secure earlier work. Check prerequisite understanding and the learner's readiness before assigning extension tasks. Require derivations, accurate diagrams and varied practice; a correct short example is not full assessment evidence. Exam-board and tier-specific pathways are outside this edition.
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