Cube Root 1 to 30

As we saw earlier, if we take the number x, the cube root y of the number x will be that number that has to be multiplied three times to get the number x.

If we have to represent it using mathematics,

x=y × y × y

x=y3

So y=3√x

So we can write that y is the cube root of x.

Now we will see some sub-topics related to the cube-root of a number.

Perfect Cube

A number x is called a Perfect Cube if its cube root is the same number and is an integer. 

For example, 64 is a Perfect Cube because it is the cube of three equal and integer numbers which are 4, 4, and 4.

64=4 × 4 × 4

64=43

4=3√64

Similar examples of Perfect Cubes are 125, 1000, 512, etc.

Another way to define a Perfect Cube is, Perfect Cube is described as a number that is equal to the same number three times.

Perfect Cubes can be found by the method of factorization.

A point to note is that the cube root of a Perfect Cube is the same number which is multiplied three times to get the Perfect Cube. A cube root is a natural number and not a fraction.

Perfect Cubes have an excellent use and that use is in finding the volume of a cube.

Now we will move on to the main sub-topic of Cube Root in which we will see all things related to the Cube Root.

Cube Root-

We have learned in earlier topics about what a cube root is and what is the symbol of a Cube Root. Now we will see how to calculate the Cube Root and some other topics related to the Cube Root. The Cube Root of a particular number can be calculated by three methods. The first method is The Prime Factorization Method. The second method is the long-division method. The third method is The Estimation Method.

First, we will see the prime factorization method. The prime factorization method works as follows. First, we take the Prime Factors of a number then we group the same number into a group of three, using that group we can easily calculate the Cube Root of the number. Now we will see an example to calculate the Cube Root of a number using the Prime Factorization Method. 

Suppose we take a number 125,

125=5×5×5

125=53

5=3125

We have taken 5 because 5 is the Prime Factor of 125.

Now we will see how to calculate the Cube Root of a large number which is a perfect cube using The Estimation Method.

For example, we take a large number 2197 this number is a large number and it is a perfect cube.

Upon Observation, we see that the digit at the Units Place in 2197 is 7.

Now when we see the Cube Table, we come to know that the cube of a number that has 7 at the unit’s digit is 3.

What I mean is 33=27

So this basically means that when we calculate the cube root of 2197, that number will have 3 at the unit’s place.

Now, upon ignoring the last three digits of 2197, that is ignoring 1, 9, and 7. Now when we consider 2 as the reference number. We know from basic mathematics that 2 lies between 1 and 8 in the cube root table.

Between 1 and 8 we will choose the lower number which is 1. So now we have got the two digits of the cube root of 2197 which are 1 and 3.

So 32197 = 13.

We have taken a large number 857375, this number is a large number and is a perfect cube.

So we first split this number into two groups of three digits, 857 and 375.

The cube root of 375 will give us the unit’s digit of the cube root of 857375.

The cube root of 857 will give us the hundreds of digits of the cube root of 857375.

Since 375 has 5 at the unit digit its cube root will also give 5 at the units digit.

Now when we consider the set of three digits 857, we realize that 857 lies between 9 and 10 in the cube root table.

From 9 and 10 we will take the lower number is 9. So we have got both the digits of our cube root of 857375, which are 9 and 5.

So 3857375= 95.

Now we will how to calculate the cube roots of numbers that are not perfect cubes.

Suppose we consider the example of the number 150.

Just from observation, we can say that this is not a perfect cube. 

We can only devise from the simple observation that 150 lies between the cube of 5 which is 125 and the cube of 6 which is 216.

So now we have to subtract the smaller number from the greater number. So we subtract 5 from 6. 

6-5=1

Divide the difference by 3.

So (1/3) =0.3333

Now we have added the lower number and the quotient.

5+0.33=5.33

So the cube root of 150 is 5.3

Therefore, 

3150=5.3

Now we will look at the Cube Roots of Numbers between 1 and 30.

Cube Roots of numbers between 1 and 30

Conclusion

As discussed earlier, We talked about what Cube Root is. We started with the concept of Perfect Cubes. Then we moved on to the concept of Cube Root. Finally, we looked at the Cube Roots of the numbers between 1 and 30.