How to Calculate Cube Root Easily: We will be solving the cube root in 2 parts. First, we shall solve the right-hand part of the answer, and then we shall solve the left-hand part of the answer. If you wish you can solve the left-hand part before the right-hand part. There is no restriction on either method but generally, people prefer to solve the right-hand part first.
How to Calculate Cube Root Easily (Secret Trick)
As illustrative examples, we shall take four different cubes.
(Q) Find the cube root of 287496.
We shall represent the number 287496 as 287|496
• Next, we observe that the cube 287496 ends with a 6 and we know that when the cube ends with a 6, the cube root also ends with a 6. Thus our answer at this stage is 6. We have thus got the right-hand part of our answer.
. To find the left-hand part of the answer we take the number which lies to the left of the slash. In this case, the number lying to the left of the slash is 287. Now, we need to find two perfect cubes between which the number 287 lies in the number line. From the key, we find that 287 lies between the perfect cubes 216 (the cube of 6) and 343 (the cube of 7).
Now, out of the numbers obtained above, we take the smaller number and put it on the left-hand part of the answer. Thus, out of 6 and 7, we take the smaller number 6 and put it beside the answer of __6 already obtained. Our final answer is 66. Thus, 66 is the cube root of 287496.
(Q) Find the cube root of 205379.
• We represent 205379 as 205 379
• The cube ends with a 9, so the cube root also ends with a 9. (The answer at this stage is 9.
The part to the left of the slash is 205. It lies between the perfect cubes 125 (the cube of 5) and 216 (the cube of 6) • Out of 5 and 6, the smaller number is 5 and so we take it
as the left part of the answer. The final answer is 59.
(Q) Find the cube root of 681472.
• We represent 681472 as 681 472
• The cube ends with a 2, so the root ends with an 8. The answer at this stage is 8.
• ‘681 lies between 512 (the cube of 8) and 729 (the cube of 9).
• The smaller number is and hence our final answer is 88. (Q) Find the cube root of 830584.
• The cube ends with a 4 and the root will also end with a 4.
• 830 lies between 729 (the cube of 9) and 1000 (the cube of 10).
Since the smaller number is 9, the final answer is 94.
You will observe that as we proceeded with the examples, we took much less time to solve the cube-roots. After some practice, you will be able to solve the cube-roots by mere observation of the cube and without the necessity of doing any intermediary steps.
It must be noted that immaterial of the number of digits in the cube, the procedure for solving them is the same.
(Q) Find the cube root of 2197.
• The number 2197 will be represented as 2 197 • The cube ends in 7 and so the cube root will end with a 3. We will put 3 as the right-hand part of the answer. • The number 2 lies between 1 (the cube of 1) and 8 (the cube of 2).
• The smaller number is 1 which we will put as the left-hand part of the answer. The final answer is 13.
We may thus conclude that there exists only one common procedure for solving all types of perfect cube-roots.
In my seminars, the participants often ask what is the procedure for solving cube roots of numbers having more than 6 digits. (All the examples that we have solved before had 6 or fewer digits.)
Well, the answer to this question is that the procedure for solving the problem is the same. The only difference, in this case, is that you will be expanding the number line.