Cube Roots: Vedic Maths | Improve Your Calculations: Vedic Maths (English) - Class 6 PDF Download

Cube Root

Cube root is the number that needs to be multiplied three times to get the original number. Cube root is an inverse operation of the cube of a number.
It is the reverse process of the cube of a number and is denoted by ∛. Here the word Root represents the primary source or origin of the cube. The other way to denote cube root is to write 1/3 as the exponent of a number.
So, we just need to find out the cube of which number should be taken to get the given number. The cube root formula is ∛x = y. Where y is the cube root of x.

Cube Root of Numbers

To calculate cube root we need to Memorize the cubes of unit digit and its relations from 1 to 10. In fact, cube root is easier than square root, provided you have a cube of 1 to 10 in your mind.
Remember the following cubes in mind
1³ = 1
2³ = 12
3³ = 27
4³ = 32
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
10³ = 1000
Also remember:
When the last digit of a cube root is 8 then the unit digit will be 2, and vise versa
2 —— 8
8 —— 2
Same case goes with 7 and 3
7 —— 3
3 —— 7
Other than these 4 numbers 2, 3, 7, 8 all other digits give the same unit digit. E.g.
1 — 1
4 — 4
5 — 5
6 — 6
9 — 9
Now let’s see how we can make use of these.

Example 1: ∛12167

Ans: Step 1: Separate the number in two parts three digits each. If two digits remain at last, then put one 0 before the number and make it a group of three digits.
∛ 12167 = 012, 167
Step 2: Here the last digit is 7 then the unit digit will be 3 (as discussed earlier)
Step 3: Now see the remaining 12 comes under which digit cubes. In this case 12 comes between the cube of 2³ and 3³. So take the lower one 2
Step 4: Join results obtained from step 2 and step 3. That is 2 and 3. So answer is 23

Example 2: ∛970299

Ans: Step 1: Two groups 970 and 299. Last digit is 9 so unit digit will also comes 9
Step 2: Group 970 comes under 9³ and 10³. So take smaller one 9
Step 3: Join results obtained from step 1 and step 2. 99 is the Answer

Example 3: ∛551368

Ans: ∛551368
Step 1: 551 and 368. Last digit is 8 so unit digit will be 2
Step 2: 551 comes under 8³ (512) and 9³ (729). So take smaller one that is 8
Step 3: Join result of step 2 and step 1, that is 82. Answer is 82

Example 4: ∛19683 + ∛2197

Ans: Step 1: ∛19683 = 27
Step 2: ∛2197 = 13
Step 3: Add results obtained from step one and two. 27 + 13 = 40