Cube root of 3375 -Different methods

What do you mean by Cube root of 3375?

When a number is multiplied by itself three times to give a product of 3375, then that number is the cube root of 3375.

3375 = 15 × 15 × 15

Now we can see that the cube root of 3375 is 15

It can be also written as\sqrt[3]{3375} \text { or } 3375^{1 / 3}

We are going to find out the cube root using two methods:

1. Prime factorization method
2. Estimation method

Prime factorisation method

This is the easiest method to find out the cube roots but it becomes quite lengthy when we have to find cube roots of large numbers.

We have to follow the following steps

1. First, we have to do the prime factorisation of 3375. It is usually done by dividing the number by the smallest possible prime factor. In this case, we have to divide it by 3 first. We have to divide it by prime numbers until the last quotient is 1. It is done as follows.

2. Now we can write,

3375 = 3 × 3 × 3 × 5 × 5 × 5

3. After getting the prime factors we have to divide them into groups of threes containing the same factors.

Here the first group contains 3 × 3 × 3 and the second group contains 5 × 5 × 5

3375 = (3 × 3 × 3) × (5 × 5 × 5)

4. Now we have to take 1 number from each group.

Here we take 3 from the first group and 5 from the second group.

5. We have to multiply the factors we got from each group.

This product is the cube root of 3375.

Estimation method

This method takes less time as compared to the previous one. We can use it for finding cube roots of large numbers that are perfect cubes.

We have to follow the following steps

1. First, the number is divided by making groups of three digits from the right side.

If the last group on the left side doesn’t have 3 digits, it is okay and we will consider that group as it is.

Two groups are formed in this case as shown below. 375 is the first group and 3 is the second group.

3 3 7 5

2. The unit place of the first group from the right determines the unit place of the cube root of the number.

Refer to the following lookup table 

So, the unit place of the first group 375 is 5. By referring to the above table, we know that the unit place of the \sqrt[3]{3375} \text { is } 5.

3. Now we will look at the second group from the right.

It contains only 1 digit i.e., 3.

3 lies between the \left(1^{3}=1\right) \text { and }\left(2^{3}=8\right) \text { and the smaller number is }\left(1^{3}=1\right) \text {. }

Hence, the digit in the tens place of \sqrt[3]{3375} \text { is } 1.

4. Therefore we can conclude that 15 is the \sqrt[3]{3375}.

Solved Examples

1. What is the cube root of 27000?

Solution:

27000 = 3375 × 8

\sqrt[3]{27000}=\sqrt[3]{(3375 \times 8)}

\sqrt[3]{27000}=\sqrt[3]{(3375)} \times \sqrt[3]{(8)}

We already know that \sqrt[3]{3375} \text { is } 15 \text { and } \sqrt[3]{8} \text { is } 2

\sqrt[3]{27000}=15 \times 2

\sqrt[3]{27000}=30

2. What is the length of each side of a cube if its volume is 3375 m³?

Solution:

The volume of a cube = side × side × side

Side = cube root of the volume 

         = \sqrt[3]{3375}

         = 15 \mathrm{~m}