Take Cube Roots of 6-Digit Numbers Mentally

Step 7 A Few Examples and Practice

Like any trick, you will need to practice the cube root extraction technique a few times before you can really crank them out mentally. A veteran of the technique will be able to extract these numbers in ~2 seconds or less. Below are a few abbreviated examples, followed by a couple of numbers for you to try to take the cube roots of:

Example 1: 970,299
Splitting this number at the comma, we evaluate the two halves: 970, and 299. 299 ends in a 9, as does 9³, so the 1's digit of the cube root is 9. 970 falls between 2 cubes: 729 (9³) and 1000 (10³). Picking the lower one, we get a 10's digit of 9. Thus, the cube root of 970,299 is 99.

Example 2: 91,125
Using the same split technique as above, we split the number into 2 halves: 91 and 125. 125 ends in a 5, as does 5³, so the 1's digit is 5. 91 falls between 64(4³) and 125(5³). Picking the lower one, we get a 10's digit of 4, thus the cube root of 91,125 is 45.

Example 3: 512,000
This example adds one small caveat to our previous knowledge. As you can see, the left hand side of the cube is 512, a perfect cube. If that's the case, pick the cube that is the same as this perfect cube (in this example, 8³ = 512, so we get a 10's digit of 8). Then, for the right hand side, 0³ is of course 0, so the 1's digit is 0. Evaluating, we get a cube root of 80.

Here are a few more you can try, answers in the next step:
1) 2,744
2) 704,969
3) 148,877
4) 474,552
5) 24,389
6) 39,304
7) 68,921