Grade 8 Cubes and Cube Roots Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Find the Cube Roots of the Given Numbers

(a)

(2) Find the Cube Roots of the Given Numbers

(a)

(3) Find the Cube Roots of the Given Numbers

(a)

(4) Find the Cube Roots of the Given Numbers

(a)

(5) Evaluate the Following

(a)

(6) Evaluate the Following

(a)

(7) Evaluate the Following

(a)

(8) Each Number Given is Not a Perfect Cube. Find the Smallest Number (M) It Must be Multiplied by to Make It a Perfect Cube. Also Find the Smallest Number (D) It Must be Divided by to Make It a Perfect Cube

(a)

(9) Each Number Given is Not a Perfect Cube. Find the Smallest Number (M) It Must be Multiplied by to Make It a Perfect Cube. Also Find the Smallest Number (D) It Must be Divided by to Make It a Perfect Cube

(a)

(10) Each Number Given is Not a Perfect Cube. Find the Smallest Number (M) It Must be Multiplied by to Make It a Perfect Cube. Also Find the Smallest Number (D) It Must be Divided by to Make It a Perfect Cube

(a)

(11) Each Number Given is Not a Perfect Cube. Find the Smallest Number (M) It Must be Multiplied by to Make It a Perfect Cube. Also Find the Smallest Number (D) It Must be Divided by to Make It a Perfect Cube

(a)

(12) Each Number Given is Not a Perfect Cube. Find the Smallest Number (M) It Must be Multiplied by to Make It a Perfect Cube. Also Find the Smallest Number (D) It Must be Divided by to Make It a Perfect Cube

(a)

(13) Write the Units Digit of the Following

(a)

(b)

(c)

(14) Write the Units Digit of the Following

(a)

(b)

(c)

(15) the Volume of a Cubical Box is 117649 Meter Cube (M3) . What is the Length of Each Side of the Cube?

(16) if the Length of Each Side of a Cube is Reduced to One Third of Its Original Value, then Express Its New Volume as a Fraction of Its Original Volume

Answers and Explanations

Answer 1 (A)

  • For the cube root first we identify its prime factor as below,

  • Now for cube root:

Answer 2 (A)

  • Cube root of
  • For the cube root first we identify its prime factor as below

  • Now,

Answer 3 (A)

  • For the cube root of

  • Prime factor of 512 are,

  • Prime factor of 5832 are,

  • So,

Answer 4 (A)

  • For the cube root of,

  • Now, prime factor of 592704 are,

  • Now, prime factor of 74088 are,

  • Now,

Answer 5 (A)

  • Given equation,

  • Now first,

  • Now,

  • Now,

  • Now,

Answer 6 (A)

  • Given equation,

  • Now,

  • Now,

  • Now,

  • Then ,

Answer 7 (A)

  • Now,

  • Then,

  • Now,

  • Now,

  • Now,

Answer 8 (A)

  • Here given number is 5400.
  • Now perfect cube number is a number of multiplication of three identical integer numbers.
  • For find out the identical number; list out its prime factor
  • So,
  • From above its clear that “5” remains without pair of three identical number
  • So, smallest number that must multiply to make number 5400 perfect cube is: “5”
  • So,
  • And, smallest number that must divide to make number 5400 perfect cube is:
  • So,
  • Therefore, the answer is

Answer 9 (A)

  • Here given number is 18522.
  • Now perfect cube number is a number of multiplication of three identical integer number.
  • For find out the identical number; list out its prime factor
  • So,

  • From above its clear that “” remains without pair of three identical number
  • So, smallest number that must multiply to make number 18522 perfect cube is: “
  • So,
  • And, smallest number that must divide to make number 18522 perfect cube is:
  • So,
  • Therefore,

Answer 10 (A)

  • Here given number is 3316.
  • Now perfect cube number is a number of multiplication of three identical integer number.
  • For find out the identical number; list out its prime factor
  • So,

  • From above its clear that “” remains without pair of three identical number
  • So, smallest number that must multiply to make number 3136 perfect cube is: “
  • So,
  • And, smallest number that must divide to make number 3136 perfect cube is:
  • So,
  • Therefore,

Answer 11 (A)

  • Here given number is 1372.
  • Now perfect cube number is a number of multiplication of three identical integer number.
  • For find out the identical number; list out its prime factor
  • So,

  • From above its clear that “” remains without pair of three identical number
  • So, smallest number that must multiply to make number 1372 perfect cube is: “
  • So,
  • And, smallest number that must divide to make number 1372 perfect cube is:
  • So,
  • Therefore,

Answer 12 (A)

  • Here given number is 8232.
  • Now perfect cube number is a number of multiplication of three identical integer number.
  • For find out the identical number; list out its prime factor
  • So,

  • From above its clear that “” remains without pair of three identical number
  • So, smallest number that must multiply to make number 8232 perfect cube is: “
  • So,
  • And, smallest number that must divide to make number 8232 perfect cube is:
  • So,
  • Therefore,

Answer 13 (A)

  • Here consider cube of last digit (unit digit) only;

  • Here 8 itself is a unit digit.
  • So,

Answer 13 (B)

  • Here consider cube of last digit (unit digit) only;

  • Here from 729; 9 is at unit place.
  • So,

Answer 13 (C)

  • Here consider cube of last digit (unit digit) only;

  • Here from 64; 4 is at unit place.
  • So,

Answer 14 (A)

  • To identify the unit digit of given number cube root, first we should know the cube of the unit digit.
  • That means
  • Now,

  • Here to identify the unit digit of cube root of given number we consider only last digit (unit digit) of given number;
  • Now, we know that
  • Therefore,

Answer 14 (B)

  • To identify the unit digit of given number cube root, first we should know the cube of the unit digit.
  • That means
  • Now,

  • Here to identify the unit digit of cube root of given number we consider only last digit (unit digit) of given number;
  • Now, we know that

Answer 14 (C)

  • To identify the unit digit of given number cube root, first we should know the cube of the unit digit.
  • That means
  • Now,

  • Here to identify the unit digit of cube root of given number we consider only last digit (unit digit) of given number;
  • Now, we know that

Answer (15)

  • Volume of the cubical box
  • Now we know that, volume of cube
  • So,

Volume of the cubical box

  • Now, for cube root of 117649 ,

  • Now,

  • So, length of each side of cubical box is 49 m

Answer (16)

  • Suppose length of each side of cube
  • Now,

Volume of cube

  • If its length reduced by one third of its original length
  • Than;

  • Now

  • Therefore,

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