Mental Improvment Forum > Calculation Techniques > Finding Cube Roots

Firstly, you need to memorize the following list, which is very easy.

1³=1

2³=8

3³=27

4³=64

5³=125

6³=216

7³=343

8³=512

9³=729

Now lets try the following example:

³√15625=?

The first step is to separate the number 15625 into groups of three from right to left, so:

15 625

Now take the number 15 and compare it to the memorized chart of cubes. You will see that the largest cube which goes into 15 if 2³. So the first digit of your answer is a 2. Finally, take the other grouping, 625, and compare it's last digit, 5, to the last digits of the chart. The only option is 125, which is the product 5³. So the answer is 25!

³√15625=25

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Another example

³√941192=?

941 192

The biggest cube that goes into 941 is 9, so the first digit is 9. The other groups last digit is 2. The only cube that ends in 2 is 8³. So the last digit in the answer is 8. The number follows as 98.

³√941192=98

1³=1

2³=8

3³=27

4³=64

5³=125

6³=216

7³=343

8³=512

9³=729

Now lets try the following example:

³√15625=?

The first step is to separate the number 15625 into groups of three from right to left, so:

15 625

Now take the number 15 and compare it to the memorized chart of cubes. You will see that the largest cube which goes into 15 if 2³. So the first digit of your answer is a 2. Finally, take the other grouping, 625, and compare it's last digit, 5, to the last digits of the chart. The only option is 125, which is the product 5³. So the answer is 25!

³√15625=25

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Another example

³√941192=?

941 192

The biggest cube that goes into 941 is 9, so the first digit is 9. The other groups last digit is 2. The only cube that ends in 2 is 8³. So the last digit in the answer is 8. The number follows as 98.

³√941192=98