I request the students to memorize the cubes of numbers 1 to 10.

The list is below:

1 1

2 8

3 27

4 64

5 125

6 216

7 343

8 512

9 729

10 1000

Remeber the last digit of the cubes for the corresponding number. Like the number 7 and last digit 3

On the basis of above cube roots we can draw the conclusion as below.

The last digit of the cube The last digit of the cube root

1 1

2 8

3 7

4 4

5 5

6 6

7 3

8 2

9 9

0 0

We can conclude that all cubes end with the same number except 3, 7 and 2

Method:

If the cube given to you is 39304, split it into 39|304.

Q.) Cube root of 287496

A.) Split it to 287|496. Since it ends in 6, the cube root also ends in 6, so now we have the right hand part.

Now take the part on LHS i.e.: 287. We need two perfect cubes between which the number 287 lies.

From the above table we find that 287 lies between 216 (6^3) and 343 (7^3).We take the smaller number 6 and put it in the left hand part of our number. Thus the answer is 66.

Q.) 205379

A.) Split 205|379.

The cube ends in 9. So the root also ends in 9. Left hand part is 205. It lies between 125 and 216. Out of 5 and 6 we take the smaller number and put it on the left hand side of the answer.

Thus our answer is:** 59**