Easy How to Find a Cube Too
Importance of Cube/Cube Roots In Bank Exams
- It is one of the basic things a bank aspirant should know.
- You can find its application extensively while solving simplification & approximation questions.
- By learning the short tricks to find the cube/cube roots of a number, you can save time in the exam.
- So you can maximize your attempts.
Shortcut to find Cube
Candidates who are preparing for competitive exams should remember tables up to 30, squares, and cubes up to 20. This makes your calculation easier as well as quicker. Now, let's have a look at cubes up to 20.
| 1 to 10 cubes | 11 to 20 cubes |
| 13 = 1 | 113 = 1331 |
| 23 = 8 | 123 = 1728 |
| 33 = 27 | 133 = 2197 |
| 43 = 64 | 143 = 2744 |
| 53 = 125 | 153 = 3375 |
| 63 = 216 | 163 = 4096 |
| 73 = 343 | 173 = 4913 |
| 83 = 512 | 183 = 5832 |
| 93 = 729 | 193 = 6859 |
| 103 = 1000 | 203 = 8000 |
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Now, let`s have a look at the trick to solve the cubes.
We all know, to solve the cube of a number, we use the formula (a + b)3 which is a3 + 3a2b + 3ab2 + b3 .
Now, we will be using this method only but in a smart way so that you can find out the cube in cubes can be solved in exams in just a few seconds and without writing all the steps. So, you have to do the complete calculation in a single go.
I: Think the above formulae as a3 | 3a2b | 3ab2 | b3. We have divided the formulae into four parts.
II: Then just calculate all these four parts and write their values.
III: Now, keep only one rightmost digit in each part from the right side and carry forward the extra digits to the previous left parts.
Let's have a look at some examples following the above steps for better understanding:
1. (23)3 :
I: 23 | 3. 22 . 3 | 3. 2 . 32 | 33
II: 8 | 36 | 54 | 27
III:= 124 1 5 6 2 7
(Kept rightmost digit of each part from the right-hand side and Carry forward extra digits to the previous left part)
Start from the right side,
In 27; 7 will be written and 2 will be carried 54.
Then 54 + 2 = 56. Now, 6 will be written and 5 carry forward to 36.
It will be 36 + 5 equals 41. Again, 1 will be written and 4 will be carried forward.
Finally, 8 + 4 is 12. Combining all, the cube of 23 is 12167.
Answer: 12167
2. (68)3 :
I: 63 | 3. 62 . 8 | 3. 6 . 82 | 83
II: 216 | 864 | 1152 | 512
III:= 31498 4 120 3 51 2
(Kept rightmost digit of each part from the right-hand side and Carried forward extra digits to the previous left part)
Start from the right side, in 512; 2 will be written and 51 will be carried 1152.
Then 1152 + 51 = 1203. Now, 3 will be written and 120 carry forward to the 864.
It will be 864 + 120 equals 984. Again, 4 will be written and 98 will be carried forward.
Finally, 216 + 98 is 314. Combining all, the cube of 68 is 314432.
Answer: 314432
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3. (109)3 :
I: 103 | 3. 102 . 9 | 3. 10 . 92 | 93
II: 1000 | 2700 | 2430 | 729
III:=1295 295 0 250 2 72 9
(Kept rightmost digit of each part from the right-hand side and Carried forward extra digits to the previous left part)
Start from the right side, in 729; 9 will be written and 72 will be carried to 2430.
Then 2430 + 72 = 2502. Now, 2 will be written and 250 carry forward to 2700.
It will be 2700 + 250 equals 2950. Again, 0 will be written and 295 will be carried forward.
Finally, 1000 + 295 is 1295. Combining all, the cube of 68 is 1295029.
Answer: 1295029
By breaking the formula and solving it in parts make your calculation easier. Don`t forget to add carry forwarded values.
Let`s have a look at another way of using the formulae and another trick to solve the cubes
I: Write the numbers in the form ofa3 | a2b | ab2 | b3
II: Calculate above values
II: Double (Multiply by 2)the second and third part from any of the sides.
III:Now, adding the result of both the steps, write the final answer keeping only one digit at each part starting from the right-hand side.
Example: (64)3
I: 63 | 62 . 4 | 6 . 42 | 43
II: 216| 144 | 96 | 64
III: | 288 | 192 | (144 and 96 are multiplied by 2)
IV: 26246 129 46 4(Added II and III Steps)
In the above example, start from the right hand side, 4 is written and 6 is carried to (96 + 192 = 288).
Then 288 + 6 carry = 294. Now, 4 will be written and 29 is again carried to (144 + 288 = 442).
Then 442 + 29 carry = 461. Now, 1 will be written and 46 will be added to 216.
Then 216 + 46 equal to 262. Combining all cube of 64 is 262144.
Answer: 262144
Example:(112)3
I: 113 | 112 . 2 | 11 . 22 | 23
II: 1331|242 |44 | 8
III: 484 | 88 (242 and 44 are multiplied by 2)
IV: 1404 73 9 13 2 8 (Added II and III Steps)
Start from the right-hand side, 8 is a single digit so it is written.
Then in (44 +88) = 132, 2 will be written and 13 will be carry forward to previous part i.e, (242 +484) equals 726.
Now, 726 + 13 carry = 739. After that 9 is written and 73 carry forward to 1331
1331 +73 equal to 1404. Combining all cube of 112 is 1404928.
Answer: 1404928
Example: (98)3
I: 93 | 92 . 8 | 9 . 82 | 83
II: 729| 648 | 576 | 512
III: 1296 | 1152 (648 and 576 multiplied by 2)
IV: 94121211779512 (Added II and III Steps)
Start from the right-hand side, in 512, 2 is written and 51 carry forward to (576 + 1152 = 1728)
Then 1728 + 51 carry equals 1779. Now 2 is written and 177 carry forward to (648 + 1296 = 1944)
Then 1944 + 177 carry = 2121. Again only digit i., 1 is written and 212 is carried forward.
Finally, 212 + 729 is equal to 941.
Combining all cube of 98 is 941192.
Answer: 941192
Calculate the values of cubes of the numbers using these tricks easily. Make sure that you don't write all the steps in the exam. Just calculate the steps in your mind and answer it quickly.
Solve the following cubes and post your answer in the comment section:
1. (218)3
2. (77)3
3. (111)3
4. (305)3
5. (83)3
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Source: https://byjusexamprep.com/short-tricks-to-find-cube-number-i
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