CBSE Class 8

On this page, you will find Cubes and Cube Roots Class 8 Notes Maths Chapter 7 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 7 Cubes and Cube Roots will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 7 Notes Cubes and Cube Roots

Cubes and Cube Roots Class 8 Notes Conceptual Facts

• A natural number n is a perfect cube if there exists a natural number m such that m x m x m = n For example: 1, 8, 27 …. are all perfect cubes

Properties of Cubes of Numbers:

• Cubes of all odd numbers are odd. Thus 3³ = 27, 5³ = 125, etc.
• Cubes of all even numbers are even. Thus 2³ = 8, 4³ = 64, 6³ = 216, etc.
• Cubes of all negative numbers are always negative. Thus (-1)³ = -1, (-2)³ = -8, (-3)³ = -27, etc.
• \(\left(\frac{a}{b}\right)^{3}=\frac{a^{3}}{b^{3}}\)

Properties of Cube Roots:

(i) \(\sqrt[3]{-a^{3}}=-a\)

(ii) \(\sqrt[3]{a b}=\sqrt[3] a^{a} \sqrt[3]{b}\)

(iii) \(\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}, b \neq 0\)

A Pattern of Cube:

1³ = 1
2² = 8 = 3 + 5
3³ = 27 = 7 + 9 + 11
4³ = 64 = 13 + 15 + 17 + 19
5³ = 125 = 21 + 23 + 25 + 27 + 29

On this page, you will find Squares and Square Roots Class 8 Notes Maths Chapter 6 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 6 Squares and Square Roots will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 6 Notes Squares and Square Roots

Squares and Square Roots Class 8 Notes Conceptual Facts

1. If a number is multiplied by itself, the product that we get is called the square of the number.
For example:
4 x 4 = 4² = 16                                                                 (16 is square of 4)
20 x 20 = 20² = 400                                                         (400 is square of 20)
\(\frac{3}{5} \times \frac{3}{5}=\left(\frac{3}{5}\right)^{2}=\frac{9}{25}\) \(\left(\frac{9}{25} \text { is square of } \frac{3}{5}\right)\)

2. Square of a number is represented as the number raised to the power 2.

3. A perfect square is a number that can be expressed as the product of two equal integers.
For example: 1, 4, 9, 16, 25, …, are all perfect square numbers.

4. Properties of square numbers:
(i) No square number ends with the digits 2, 3, 7 or 8 at its unit places.

(ii) The square numbers must end with the digits 0, 1, 4, 5, 6, 9 but the number ending with 0, 1, 4, 5, 6, 9 may or may not be a perfect number.
For example: 36 is a perfect square but 56 is not.
256 is a perfect square but 346 is not.

(iii) Square of even number is always an even and the square of odd number is odd.
For example:
4² = 16(even)
5² = 25(odd)

(iv) A perfect square can never be a negative number.

(v) For every natural number n, (n + 1)² – n² – (n + 1) + n
For example: 14² -13² = (13 + 1) + 13 = 14 + 13 = 27
26² – 25² = (25 + 1) + 25 = 26 + 25 = 51

5. Pythagorean Tripletr: A triplet (m, n,p) is called a Pythagorean triplet if m² + n² = p²
For example: (3, 4, 5), (8, 15, 17) and (20, 21, 29)
Product of two consecutive even or odd natural numbers:
Example:
11 x 13 = 143 – 12² – 1 (product of odds)
13 x 15 = 195 = 14² – 1 (product of odds)
44 x 46 = 2024 = 45² – 1 (product of evens)

Some Patterns in square numbers:

On this page, you will find Data Handling Class 8 Notes Maths Chapter 5 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 5 Data Handling will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 5 Notes Data Handling

Data Handling Class 8 Notes Conceptual Facts

1. Data: Collection of information as numerical facts about the objects or events is called Data.

2. Types of Data: Discrete and continuous.

3. Frequency: The number of times each score occurs is called frequency.

4. Range: The difference between the greatest and the least observations is called the Range.

5. Relative Frequency: The ratio of the frequency of each item to the sum of all frequencies is called Relative frequency.
\(\text { Relative frequency }=\frac{\text { Frequency of an object }}{\text { Total frequency }}\)

6. Class-size: Difference between upper and lower limits of a class interval is called class-size.

7. Class-mark: Mid value of class interval is called its class-mark.
\(\text { Class-mark }=\frac{\text { Upper limit }+\text { Lower limit }}{2}\)

8. Class-frequency: The frequency of a particular class-interval is called class-frequency.

9. Bar Graph: Horizontal and vertical Histogram: Horizontal and vertical

10. Pie chart: Pie chart is a way of representing the data in the form of sectors of a circle.
Central angle for a sector = \(\left(\frac{\text { Value of the component }}{\text { Total value }} \times 360\right)^{\circ}\)

On this page, you will find Practical Geometry Class 8 Notes Maths Chapter 4 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 4 Practical Geometry will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 4 Notes Practical Geometry

Practical Geometry Class 8 Notes Conceptual Facts

Construction of four-sided figures when

• Four sides and one diagonal are given.
• Two diagonals and three sides are given.
• Two adjacent sides and three angles are given.
• Three sides and two included angles are given.

Some special cases:

• To construct a square when only one side is given.
• To construct a trapezium.

Quadrilaterals basically has ten parts in all, four sides, four angles and two diagonals.

To construct a quadrilateral, we need the measurement of five specified parts.

Before constructing a figure, we need to draw a rough free hand sketch.

Using the properties of the quadrilateral, we can construct parallelograms, squares, rectangles, rhombuses and trapeziums.

On this page, you will find Understanding Quadrilaterals Class 8 Notes Maths Chapter 3 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 3 Understanding Quadrilaterals will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 3 Notes Understanding Quadrilaterals

Understanding Quadrilaterals Class 8 Notes Conceptual Facts

Polygon: A simple closed curve made up of only line segments is called a polygon.
Examples of Polygons:
(i) Triangle

(ii) Quadrilateral

(iii) Pentagon

(iv) Hexagon

Convex and concave polygons

Regular and irregular polygons

Angle sum property: The sum of three angles of a triangle is 180° In AABC, ∠A + ∠B + ∠C = 180°

Sum of all the exterior angles of a polygon is 360°. In the given polygon ABODE, exterior angles ∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 360°.

Kind of Quadrilaterals

(i) Parallelogram

Properties
(a) Opposite angles are equal
(b) Opposite sides are equal
(c) Diagonals bisect each other

(ii) Rhombus:

(a) All sides are equal
(b) Opposite angles are equal
(c) Diagonals bisect each other at 90°

(iii) Rectangle

(a) It is a parallelogram having each angle of 90°
(b) Opposite sides are equal
(c) Diagonals are equal

(iv) Square:

(a) All sides are equal
(b) Each angle is of 90°
(c) Diagonals are equal and bisect each other at 90°

(v) Kite:

(a) Diagonals are perpendicular to each other.
(b) One of the diagonals bisects the other
(c) m∠A = m∠C but m∠B ≠ m∠D

(vi) Trapezium:

A pair of opposite sides is parallel to each other.