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Home >> Cube Root >> Cube Root by Shortcut Method >>

Cube Root by Shortcut Method

Cube Root by Prime Factorization Method Cube Root by Shortcut Method

Before you study this concept, you are adviced to read:

What are Cube Numbers ?
What is a Cube Root ?
What are the Properties of Cube Numbers ?

Steps of this shortcut method are:

  • Step 1: Make group of three digits starting from the digit at oneís place of the given cube number (if the given number have five digit, you can make first group comprising three digits and second group comprising two digits)

  • Step 2: Take First Group -- Digit at Oneís place of first group will help you to find digit at oneís place of the cube root.(For this you must study all the properties of cube numbers)

  • Step 3: Take Second Group Ė Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at tenís place of the cube root

  • Step 4: Result of step 2 and step 3 gives you cube root of the given number.

    (Note: This shortcut method applies to only perfect cubes and not on non-perfect cubes)

    Example 1: Find cube root of 13824 using shortcut method
    Solution: Steps of find cube root are as follows:

  • Step 1: Make group of three digits starting from the digit at oneís place, of the given cube number ( if the given number have five digit, you can make first group comprising three digits and second group comprising two digits.)
    Here the given cube number has five digits, so we get following two groups:
    First Group = 824
    Second Group = 13


  • Step 2: Take First Group -- Digit at Oneís place of first group will help you to find digit at oneís place of the cube root.
    First Group = 824
    Oneís place digit of this first group = 4

    As per the Property 4 of Cube Number :- Cube of Natural Number ending with 4, also ends with 4. So, this means that cube root of given number 13824 will certainly have 4 at its oneís place.

  • Step 3: Take Second Group Ė Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at tenís place of the cube root
    Second Group = 13
    Cube of 2 = 8 and 8 is the nearest & less than 13

    (If we take 3 its cube is 27, which is also nearest but more than 13)
    So, this means that cube root of given number 13824 will certainly have 2 at its tenís place.

  • Step 4: Result of step 2 and step 3 gives you cube root of the given number.
    From Step 2 we get:
    Digit at oneís place = 4

    From Step 3 we get:
    Digit at tenís place = 2

    Hence, cube root of 13824 = 24



    Example 2: Find cube root of 175616 using shortcut method
    Solution: Steps of find cube root are as follows:

  • Step 1: Make group of three digits starting from the digit at oneís place of the given cube number
    Two groups:
    First Group = 616
    Second Group = 175


  • Step 2: Take First Group -- Digit at Oneís place of first group will help you to find digit at oneís place of the cube root.
    First Group = 616
    Oneís place digit of this first group = 6

    As per the Property 6 of Cube Number :- Cube of Natural Number ending with 6, also ends with 6. So, this means that cube root of given number 175616 will certainly have 6 at its oneís place.

  • Step 3: Take Second Group Ė Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at tenís place of the cube root
    Second Group = 175
    Cube of 5 = 125 and 125 is the nearest & less than 175

    (If we take 6 its cube is 216, which is also nearest but more than 175)
    So, this means that cube root of given number 175616 will certainly have 5 at its tenís place.

  • Step 4: Result of step 2 and step 3 gives you cube root of the given number.
    From Step 2 we get:
    Digit at oneís place = 6

    From Step 3 we get:
    Digit at tenís place = 5

    Hence, cube root of 175616 = 56



    Example 3: Find cube root of 110592 without using calculator
    Solution: Steps of find cube root are as follows:

  • Step 1: Make group of three digits starting from the digit at oneís place of the given cube number
    Two groups:
    First Group = 592
    Second Group = 110


  • Step 2: Take First Group -- Digit at Oneís place of first group will help you to find digit at oneís place of the cube root.
    First Group = 592
    Oneís place digit of this first group = 592

    As per the Property 8 of Cube Number :- Cube of Natural Number ending with 8, ends with 2. So, this means that cube root of given number 110592 will certainly have 8 at its oneís place.

  • Step 3: Take Second Group Ė Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at tenís place of the cube root
    Second Group = 110
    Cube of 4 = 64 and 64 is the nearest & less than 110

    (If we take 5 its cube is 125, which is also nearest but more than 110)
    So, this means that cube root of given number 175616 will certainly have 4 at its tenís place.

  • Step 4: Result of step 2 and step 3 gives you cube root of the given number.
    From Step 2 we get:
    Digit at oneís place = 8

    From Step 3 we get:
    Digit at tenís place = 4

    Hence, cube root of 110592 = 48



    Example 4: Find cube root of 300763 without using calculator
    Solution: Steps of find cube root are as follows:

  • Step 1: Make group of three digits starting from the digit at oneís place of the given cube number
    Two groups:
    First Group = 300
    Second Group = 763


  • Step 2: Take First Group -- Digit at Oneís place of first group will help you to find digit at oneís place of the cube root.
    First Group = 763
    Oneís place digit of this first group = 763

    As per the Property 7 of Cube Number :- Cube of Natural Number ending with 7, ends with 3. So, this means that cube root of given number 110592 will certainly have 7 at its oneís place.

  • Step 3: Take Second Group Ė Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at tenís place of the cube root
    Second Group = 300
    Cube of 6 = 216 and 216 is the nearest & less than 300

    (If we take 7 its cube is 343, which is also nearest but more than 300)
    So, this means that cube root of given number 175616 will certainly have 6 at its tenís place.

  • Step 4: Result of step 2 and step 3 gives you cube root of the given number.
    From Step 2 we get:
    Digit at oneís place = 7

    From Step 3 we get:
    Digit at tenís place = 6

    Hence, cube root of 300763 = 67


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