MathematicsChapter 1: Real Numbers
Irrational Q'
sqrt(2) is not equal to a/b for any integers a, b with b != 0.
Learning objectives
- Define and explain irrational q'.
- Apply irrational q' to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
sqrt(2) is not equal to ab for any integers a, b with b != 0. An isosceles right triangle with legs of side 1 has hypotenuse sqrt(12 + 12) = sqrt(2). Hippasus is the name tradition attaches to that discovery. Numbers such as sqrt(2) and pi live in Q', the irrationals.
Where / symbols
- Irrational Q'
- sqrt(2) is not equal to a/b for any integers a, b with b != 0. An isosceles right triangle with legs of side 1 has hypotenuse sqrt(1^2 + 1^2) = sqrt(2). Hippasus is the name tradition attaches to that discovery. Numbers such as sqrt(2) and pi live in Q', the irrationals.
Overview
Learn the idea, then use it:
Core Understanding
sqrt(2) is not equal to ab for any integers a, b with b != 0. An isosceles right triangle with legs of side 1 has hypotenuse sqrt(12 + 12) = sqrt(2). Hippasus is the name tradition attaches to that discovery. Numbers such as sqrt(2) and pi live in Q', the irrationals.
Examples sqrt(2) · hypotenuse · side 1 · IRRATIONAL Q': sqrt(2) is not equal to a/b for any integers a, b with b != 0. An isosceles right triangle with legs of side 1 has hypot
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — IRRATIONAL Q'
sqrt(2) is not equal to ab for any integers a, b with b != 0. An isosceles right triangle with legs of side 1 has hypotenuse sqrt(12 + 12) = sqrt(2). Hippasus is the name tradition attaches to that discovery. Numbers such as sqrt(2) and pi live in Q', the irrationals.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge irrational q' with a neighbouring idea that uses a different definition, rule, or method.
Key points
- sqrt(2)
- hypotenuse
- side 1
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Irrational Q'
Sticky Notes · Quick Revision
Core Idea
- sqrt(2) is not equal to ab for any integers a, b with b != 0.
Key Points
- sqrt(2)
- hypotenuse
- side 1
Simple Check
- Explain irrational q' in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge irrational q' with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- sqrt(2) is not equal to ab for any integers a, b with b != 0.
- sqrt(2)
- hypotenuse
- side 1
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