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Tag: CBSE 8

  • Squares And Square Roots | Study

  • Cubes And Cube Roots | Study

  • Rational Numbers | Study

  • Linear Equations In One Variable | Study

  • Class 8 | Mathematics | All In One

  • Squares And Square Roots | Study

    Squares And Square Roots | Study

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    Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 22 = 2 x 2=4(square of 2 is 4).

    If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number. (Scroll down to continue …)

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    All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place. Square numbers can only have even number of zeros at the end. Square root is the inverse operation of square.

    There are two integral square roots of a perfect square number.

    Positive square root of a number is denoted by the symbol For example, 32=9 gives

    Perfect Square or Square number: It is the square of some natural number. If m=n2, then m is a perfect square number where m and n are natural numbers. Example: 1=1 x 1=12, 4=2 x 2=22.

    Properties of Square number:

    1. A number ending in 2, 3, 7 or 8 is never a perfect square. Example: 152, 1028, 6593 etc.
    2. A number ending in 0, 1, 4, 5, 6 or 9 may not necessarily be a square number. Example: 20, 31, 24, etc.
    3. Square of even numbers are even. Example: 22 = 4, 42=16 etc.
    4. Square of odd numbers are odd. Example: 52 = 25, 92 = 81, etc.
    5. A number ending in an odd number of zeroes cannot be a perferct square. Example: 10, 1000, 900000, etc.
    6. The difference of squares of two consecutive natural number is equal to their sum. (n + 1)2– n2 = n+1+n. Example: 42 – 32 =4 + 3=7. 122– 112 =12+11 =23, etc.
    7. A triplet (m, n, p) of three natural numbers m, n and p is called Pythagorean

    triplet, if m2 + n2 = p2: 32 + 42 = 25 = 52

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  • Cubes And Cube Roots | Study

    Cubes And Cube Roots | Study

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    Cubes and Cube Root | Speed Notes

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    Cube number: Number obtained when a number is multiplied by itself three times. 23 = 2 x 2 x 2 = 8, 33 = 3 x 3 x 3=27, etc.

    Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They

    can be expressed as sum of two cubes in two different ways.

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    Numbers obtained when a number is multiplied by itself three times are known as cube numbers. For example 1, 8, 27, … etc.

    If in the prime factorisation of any number each factor appears three times, then the

    number is a perfect cube.

    The symbol

    denotes cube root. For example

    Perfect Cube: A natural number is said to be a perfect cube if it is the cube of some natural number. Example: 8 is perfect cube, because there is a natural number 2 such that 8 = 23, but 18 is not a perfect cube, because there is no natural number whose cube is 18.

    The cube of a negative number is always negative.

    Properties of Cube of Number:

    1. Cubes of even number are even.
    2. Cubes of odd numbers are odd.
    3. The sum of the cubes of first n natural numbers is equal to the square of their sum.
    4. Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.
    5. Cube of the number ending in 2 ends in 8 and cube of the number ending in 8 ends in 2.
    6. Cube of the number ending in 3 ends in 7 and cube of the number ending in 7

    ends in 3.

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  • Rational Numbers | Study

    Rational Numbers | Study

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    Rational numbers are closed under the operations of addition, subtraction and multiplication, But not in division. (Scroll down to continue …)

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    The operations addition and multiplication are
    (i) commutative for rational numbers.

    (ii) associative for rational numbers.

    The rational number 0 is the additive identity for rational numbers.

    The additive inverse of the rational number a/b is -a/b and vice- versa.

    The reciprocal or multiplicative inverse of the rational number
    is if a/b is c/d if (a/b)(c/d) =1

    Distributive property of rational numbers:

    For all rational numbers a, b and c, a(b + c) = ab + ac
    and a(b – c) = ab – ac.

    Rational numbers can be represented on a number line.

    Between any two given rational numbers there are countless rational numbers.

    The idea of mean helps us to find rational numbers between two rational numbers.

    Positive Rationals: Numerator and Denominator both are either positive or negative.

    Example: 2/3, -4/-5

    Positive Rationals: Numerator and Denominator both are either positive or negative.

    Example: -2/3, 4/-5

    .

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  • Linear Equations In One Variable | Study

    Linear Equations In One Variable | Study

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    A statement of equality of two algebraic expressions involving one or more variables. Example: x + 2 = 3

    Linear Equation in One variable: The expressions which form the equation that contain single variable and the highest power of the variable in the equation is one. (Scroll down to continue …)

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    Linear Equations in One Variable

    An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the equality sign is equal to the value of the expression on the other side.

    The equations we study in Classes VI, VII and VIII are linear equations in one variable. In such equations, the expressions which form the equation contain only one variable. Further, the equations are linear, i.e., the highest power of the variable appearing in the equation is 1.

    A linear equation may have for its solution any rational number.

    An equation may have linear expressions on both sides. Equations that we studied in Classes VI and VII had just a number on one side of the equation.

    Just as numbers, variables can, also, be transposed from one side of the equation to the other.

    Occasionally, the expressions forming equations have to be simplified before we can solve them by usual methods. Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.

    The utility of linear equations is in their diverse applications; different problems on numbers, ages, perimeters, combination of currency notes, and so on can be solved

    using linear equations.

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  • Class 8 | Mathematics | All In One

    Class 8 | Mathematics | All In One

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    Mathematics

    Unit 1(Rational Numbers)

    Unit 2(Data Handling)

    Unit 3(Square-Square Root & Cube-Cube Root)

    Unit 4(Linear Equation In One Variable)

    Unit 5(Understanding Quadrilaterals & Practical Geometry)

    Unit 6(Visualising The Solid Shapes)

    Unit 7(Algebraic Expression, Identities & Factorisation)

    Unit 8(Exponents & Powers)

    Unit 9(Comparing Quantities)

    Unit 10(Direct & Inverse Proportions)

    Unit 11(Mensuration)

    Unit 12(Introduct To Graphs)

    Unit 13(Playing With Numbers)

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