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Cubes and Cube Roots Test - 1

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Cubes and Cube Roots Test - 1
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  • Question 1
    1 / -0

    What is the cube of double of ‘a’?

    Solution

     

    Explanation:

    The  double of a = 2a

    The cube of 2a = 2a ×× 2a ×× 2a

      = 8 a3

     

     

  • Question 2
    1 / -0

    Find the cubes of 2x, 3x and 4x.

    Solution

     

    Explanation:

    The answer is 8 x3,27 x3,64 x3

    (2x) 3=2 x 2 x 2 x = 8 x3

    (3x) 3=3 x 3 x 3 x = 27 x3

    (4x) 3=4 x 4 x 4 x = 64 x3

     

     

  • Question 3
    1 / -0

    The numbers 1, 8, 27... are ____________.

    Solution

    Explanation:

    The answer is cube numbers

    As the numbers 1, 8, 27... are the cubes of 1,2 3.....

     

     

  • Question 4
    1 / -0

     A natural number is said to be a perfect cube, if it is the cube of some _________.

    Solution

    Explanation:

    The answer is natural number

    Any natural number can be a perfect cube if it is a cube of a natural number ,for example :8 is the cube of 2

     

     

  • Question 5
    1 / -0

    If ‘a’ is a non-zero number, then a × a  ×a = a3 is called ________ of ‘a’.

    Solution

    Explanation:

    The answer is cube

    When any three non-zero  same numbers are multiplied we get the cube of that number.

  • Question 6
    1 / -0

    Find the prime factorisation of 175616.

    Solution

    Explanation:

    The prime factorisation of 175616 are =

    2 × 2 ×2 × 2 ×2 × 2 ×2 × 2 ×2 ×7 ×7 × 7

     =23×23×23×73

     =  29×73 

     

     

  • Question 7
    1 / -0

    Find the ones digit of cube root of 2197.

    Solution

    Explanation:

    The answer is 3

    2197 

    Unit's place of 2197= 7

    The ones digit of cube root of 2197 will be 3 as  33=27 which has 7 as unit's place

     

  • Question 8
    1 / -0

    36x is a perfect cube number, then x = ______

    Solution

    Explanation:

    Prime factorisation of 36x = 6 × 6 × x

    Since 36x is a perfect cube , so to make it a perfect cube one 6 is needed to be put in the place of x , so that the prime factorisation of 36x becomes = 6 × 6 × 6

    So the value of x =6

  • Question 9
    1 / -0

    Find the cube of 75.

    Solution

    Explanation:

    The cube of 75 = 753

     =75 ×75 × 75
      = 421875

     

     

  • Question 10
    1 / -0

    Express 63 as the sum of odd numbers.

    Solution

    Explanation:

    63  = 6 × 6 × 6 = 216

    1 = 1= 13

    3 + 5 = 8 = 23

    7 + 9+ 11 = 27 = 33

    13 + 15 + 17 + 19 = 64 = 43

     21 + 23 +25+ 27 + 29 = 125 = 53

    31 + 33 + 35 + 37 + 39 + 41 = 216 = 63

     

     

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