Take Cube Roots of 6-Digit Numbers Mentally

Step 5 Evaluating the Cube Part 1: Right Hand Side

From the previous step, we took our number (50,653) and split it at the comma. In this step, we will evaluate the right hand side of the cube (653) to extract the 1's digit of our cube root.

The key to determining the 1's digit of the cube root is to look at the rightmost digit of the cube and compare with the rightmost digits from our list of cubes. The one's digit will then be the number from our list of cubes that matches the one's digit of the cube. So, for 653 we will want the number who's cube also ends in a 3. Looking down our list of cubes:

0³ = 0
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729

From above, we see that the cube of 7 also ends in a three, therefore, we can deduce that the cube root's 1's digit must be 7.

Now, we shall evaluate the left hand side of the cube, which we will then use to determine the number's cube root.