Cube tricks and tips for competitive exams (More Than 100)

In the last post on Cube numbers I have given the tricky method for Cubes of natural numbers (11-99) hope you have understood the Carry forward addition. As we know that cube of a natural number is the product obtained by multiplying the number three times. In this a long time is taken by the students due to long tradition method of multiplication. Now I am going give you a tricky method which will help you get the cube of a natural number more than 100 in quick time.
But as usual practice is the much needed factor of this trick otherwise the motive of giving this trick will be worthless and most importantly you have to essentially learn the cubes from 1 to 10 which is much needed for this trick.

Try to understand the concept of Carry Forward Addition again with help of demonstrations shown in this topic. Let’s now proceed with this topic:-

The trick for the natural numbers more than 100, contains nothing but an algebraic formula with proper and fixed sequence, which should not be disturbed.

Formula :- (a + b)³ = a³ +3a²b + 3ab² + b³ 

                    Where unit place digit of these numbers is taken as “b”

     & tenth including hundredth place digits of these numbers are taken as “a” together

Important thing is that the sequence of this formula should not be changed.

Revision of Cube learnt with more cubes to be learnt:-

1³  = 1 × 1 × 1 = 1.

2³ = 2 × 2 × 2 = 8.

3³ = 3 × 3 × 3 = 27.

4³ =4 × 4 × 4 = 64.

5³ =5 × 5 × 5 = 125.

6³ =6 × 6 × 6 = 216.

7³ =7 × 7 × 7 = 343.

8³ =8 × 8 × 8 = 512.

9³ =9 × 9 × 9 = 729.

10³ =10 × 10 × 10 = 1000.

11³ =11 × 11 × 11 = 1331.

12³ =12 × 12 × 12 = 1728.

13³ =13 × 13 × 13 = 2197.

14³ =14 × 14 × 14 = 2744.

15³ =15 × 15 × 15 = 3375.

Now I am giving the tricky method for calculation of Cube of Natural Numbers

Method :-

Step 1^st :- Set the given number in form of (a + b)³.

Step 2^nd :- Now expand in the sequence a³ +3a²b + 3ab² + b^3, don’t disturb or change the sequence.

Step 3^rd :- Now dissolve the expansion.

Step 4^th :- Now apply the Carry Forward Addition to get the required Cube

Demonstration of above method (Try to Understand the procedure of Carryu Forward Addition):-

101³ →   Step 1^st    Let a =10 and b =1 and set it as (10 + 1)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 1) + 3 × (10 × 1²) + 1³

               Step 3^rd   1000 + 300 + 30 + 1

               Step 4^th    Arrange it like this by applying carry forward addition →

                                1000 + (300 + 3)01 = (1000 + 30)301 = 1030301

Get the required answer 101³ = 1030301

102³ →   Step 1^st    Let a =10 and b =2 and set it as (10 + 2)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 2) + 3 × (10 × 2²) + 2³

               Step 3^rd   1000 + 600 + 120 + 8

               Step 4^th    Arrange it like this by applying carry forward addition →

                               1000 + (600+12)08 = (1000 + 61)208 = 1061208

Get the required answer 102³ = 1061208.

103³ →   Step 1^st    Let a =10 and b =3 and set it as (10 + 3)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 3) + 3 × (10 × 3²) + 3³

               Step 3^rd   1000 + 900 + 270 + 27

               Step 4^th    Arrange it like this by applying carry forward addition →

                        1000 + 900 +(270 + 2)7 = 1000 + (900 + 27)27 = (1000 + 92)727 = 1092727.

Get the required answer 103³ = 1092727.

104³ →   Step 1^st    Let a =10 and b =4 and set it as (10 + 4)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 4) + 3 × (10 × 4²) + 4³

               Step 3^rd   1000 + 1200 + 480 + 64

               Step 4^th    Arrange it like this by applying carry forward addition →

                      1000 +1200 + (480 + 6)4 = 1000 + (1200 + 48)64 = (1000 + 124)864 = 1124864.

Get the required answer 104³ = 1124864.

105³ →   Step 1^st    Let a =10 and b =5 and set it as (10 + 5)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 5) + 3 × (10 × 5²) + 5³

               Step 3^rd   1000 + 1500 + 750 + 125

               Step 4^th    Arrange it like this by applying carry forward addition →

                     1000 +1500 + (750 + 12)5 = 1000 + (1500 + 76)25 = (1000 + 157)625 = 1157625.

Get the required answer 105³ = 1157625.

106³ →   Step 1^st    Let a =10 and b =6 and set it as (10 + 6)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 6) + 3 × (10 × 6²) + 6³

               Step 3^rd   1000 + 1800 + 1080 + 216

               Step 4^th    Arrange it like this by applying carry forward addition →

                     1000 +1800 + (1080 + 21)6 = 1000 + (1800 + 110)16 = (1000 + 191)016 = 1191016.

Get the required answer 106³ = 1191016.

107³ →   Step 1^st    Let a =10 and b =7 and set it as (10 + 7)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 7) + 3 × (10 × 7²) + 7³

               Step 3^rd   1000 + 2100 + 1470 + 343

               Step 4^th    Arrange it like this by applying carry forward addition →

                    1000 +2100 + (1470 + 34)3 = 1000 + (2100 + 150)43 = (1000 + 225)043 = 1225043.

Get the required answer 107³ = 1225043.

108³ →   Step 1^st    Let a =10 and b =8 and set it as (10 + 8)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 8) + 3 × (10 × 8²) + 8³

               Step 3^rd   1000 + 2400 + 1920 + 512

               Step 4^th    Arrange it like this by applying carry forward addition →

                    1000 +2400 + (1920 + 51)2 = 1000 + (2400 + 197)12 = (1000 + 259)712 = 1259712.

Get the required answer 108³ = 1259712.

109³ →   Step 1^st    Let a =10 and b =9 and set it as (10 + 9)³

               Step 2^nd   Expand it as → 10³ + 3 ×( 10² × 9) + 3 × (10 × 9²) + 9³

               Step 3^rd   1000 + 2700 + 2430 + 729

               Step 4^th    Arrange it like this by applying carry forward addition →

                    1000 +2700 + (2430 + 72)9 = 1000 + (2700 + 250)29 = (1000 + 295)029 = 1295029.

Get the required answer 109³ = 1295029.

111³ →   Step 1^st    Let a =11 and b =1 and set it as (11 + 1)³

               Step 2^nd   Expand it as → 11³ + 3 ×( 11² × 1) + 3 × (11 × 1²) + 1³

               Step 3^rd   1331 + 363 + 33 + 1

               Step 4^th    Arrange it like this by applying carry forward addition →

                      1331 + (363 +3)31 = (1331 + 36)631 = 1367631.

Get the required answer 111³ = 1367631.

112³ →   Step 1^st    Let a =11 and b =2 and set it as (11 + 2)³

               Step 2^nd   Expand it as → 11³ + 3 ×( 11² × 2) + 3 × (11 × 2²) + 2³

               Step 3^rd   1331 + 726 + 132 + 8

               Step 4^th    Arrange it like this by applying carry forward addition →

                                1331 + (726 + 13)28 = (1331 + 73)928 = 1404928.

Get the required answer 112³ = 1404928.

113³ →   Step 1^st    Let a =11 and b =3 and set it as (11 + 3)³

               Step 2^nd   Expand it as → 11³ + 3 ×( 11² × 3) + 3 × (11 × 3²) + 3³

               Step 3^rd   1331 + 1089 + 297 + 27

               Step 4^th    Arrange it like this by applying carry forward addition →

                          1331 + 1089 + (297 + 2)7 = 1331 + (1089 + 29)97 = (1331 + 111)897 = 1442897.

Get the required answer 113³ = 1442897.

114³ →   Step 1^st    Let a =11 and b =4 and set it as (11 + 4)³

               Step 2^nd   Expand it as → 11³ + 3 ×( 11² × 4) + 3 × (11 × 4²) + 4³

               Step 3^rd   1331 + 1452 + 528 + 64

               Step 4^th    Arrange it like this by applying carry forward addition →

                         1331 + 1452 + (528 + 6)4 = 1331 + (1452 + 53)44 = (1331 + 150)544 = 1481544.

Get the required answer 114³ = 1481544.

To be continued like this upto which ever number you want to calculate but as per you preparation I would prefer you to practice for the cube of natural number upto 150 only. More than 150 is not need to be practiced although this trick suits to every natural number.

First of you should practice this trick several times and try to omit the unnecessary steps during the calculations and feel free to write for your queries and doubts.