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.
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
1^{3} = 1
2^{3} = 12
3^{3} = 27
4^{3} = 32
5^{3} = 125
6^{3} = 216
7^{3} = 343
8^{3 }= 512
9^{3} = 729
10^{3} = 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 2^{3} and 3^{3}. 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 9^{3} and 10^{3}. 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 8^{3} (512) and 9^{3} (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
36 videos31 docs3 tests

36 videos31 docs3 tests


Explore Courses for Class 6 exam
