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  • Cubes and Cube Roots | Assess

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  • Cubes and Cube Roots | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage 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… readmore

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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. (Scroll down till the end of the page).

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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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  • Diversity in the Living World | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore

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  • Life Processes | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Biology is the study of living things. All living things are called organisms, both plants and animals are living organisms. But how we decide whether something is living or non-living depends on 7 lifeprocesses. If something is living it will carryout the 7 life processes below.… readmore

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    Biology is the study of living things. All living things are called organisms, both plants and animals are living organisms. But how we decide whether something is living or non-living depends on 7 lifeprocesses. If something is living it will carryout the 7 life processes below. (Scroll down till end ..)

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  • Measurement of Length and Motion| Assess

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  • Mindful Eating: A Path to a Healthy Bodys | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore

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  • Number Play | Assess

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  • Number Play | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage We have discussed multiples, divisors, factors and have seenhow to identify factors and multiples. We have discussed and discovered thefollowing: (a) A factor of a number is an exactdivisor of thatnumber. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content (b)… readmore

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    We have discussed multiples, divisors, factors and have seenhow to identify factors and multiples. We have discussed and discovered thefollowing: (a) A factor of a number is an exactdivisor of thatnumber. (Scroll down till end of the page)

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    (b) Every number is a factor of itself. 1 is a factor ofevery number.

    (c) Every factor ofa number isless than or equal tothe given number.

    (d) Every number isa multiple ofeach of itsfactors.

    (e) Every multiple ofa given number is greater thanor equal tothat number.

    (f) Every number is a multiple of itself.

    We have learnt that – (a) The number otherthan 1, withonly factors namely 1 and thenumber itself, isa prime number. Numbers that have more than two factors are called composite numbers. Number 1is neither prime nor composite.

    (b) The number 2is the smallest prime number andis even. Every prime number other than 2 isodd.

    (c) Two numbers withonly 1 asa common factor are called co-prime numbers.

    (d) If a number is divisible byanother number thenit is divisible by each of the factors of that number.

    (e) A number divisible by two co-prime numbers is divisible by their product also.

    We have discussed how we can find just by looking at a number, whether it is divisible by small numbers 2,3,4,5,8,9 and 11.

    We have explored the relationship between digits of thenumbers and theirdivisibility by different numbers.

    (a) Divisibility by 2,5and 10 canbe seen byjust the lastdigit.

    (b) Divisibility by 3and 9 ischecked by finding the sum ofall digits.

    (c) Divisibility by 4 and 8is checked bythe last 2and 3 digits respectively.

    (d) Divisibility of11 is checked by comparing thesum of digits at odd andeven places.

    We have discovered that if twonumbers are divisible by a number then their sum and difference are also divisible by that number.

    We have learnt that – (a) The Highest Common Factor (HCF) of two ormore given numbers is the highest of their common factors.

    (b) The Lowest Common Multiple (LCM) of two ormore given numbers is the lowest of their common multiples.

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  • Physical and Chemical Changes | Assess

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