Rational and Irrational Numbers
Parallel Lines and Transversal
- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
- Properties of Angles Formed by Two Parallel Lines and a Transversal
- Axiom: If a Transversal Intersects Two Parallel Lines, Then Each Pair of Corresponding Angles is Equal.
- Axiom: If a Transversal Intersects Two Parallel Lines, Then Each Pair of Alternate Interior Angles Are Equal.
- Axiom: If a Transversal Intersects Two Parallel Lines, Then Each Pair of Interior Angles on the Same Side of the Transversal is Supplementary.
- To Draw a Line Parallel to the Given Line Through a Point Outside the Given Line Using Set-square.
- To Draw a Parallel Line to a Given Line at a Given Distance.
Indices and Cube Root
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Meaning of Numbers with Rational Indices
- Concept of Cube Number
- Concept of Cube Root
- Cube Root Through Prime Factorisation Method
Altitudes and Medians of a Triangle
Factorisation of Algebraic Expressions
Quadrilateral : Constructions and Types
Discount and Commission
Division of Polynomials
Equations in One Variable
Congruence of Triangles
Surface Area and Volume
Circle - Chord and Arc
Representation of Irrational Numbers on the Number Line:
Let us see how we can locate some of the irrational numbers on the number line.
1) Locate √2 on the number line.
Remember that √2 is the length of the diagonal of the square whose side is 1 unit.
- On the number line, point A shows the number 1. Draw line `l` perpendicular to the number line through point A.
Take point P on line `l` such that OA = AP = 1 unit.
- Draw seg OP. The ΔOAP formed is a right-angled triangle.
By Pythagoras theorem,
OP2 = OA2 + AP2 = 12 + 12 = 1 + 1 = 2.
∴ OP = √2 ....(taking square roots on both sides)
- Now, draw an arc with center O and radius OP. Name the point as Q where the arc intersects the number line. Obviously, distance OQ is `sqrt2`.
That is, the number shown by point Q is `sqrt2`.
- If we mark point R on the number line to the left of O, at the same distance as OQ, then it will indicate the number `- sqrt(2)`.
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Shaalaa.com | How to represent root 2 and root 3 on number line
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