HOW TO FIND CUBE ROOT OF A NUMBER

Definition of Cube Root :

Cube root is the inverse process of calculating the cube of a number.

It is denoted by the symbol

To obtain cube root of a number, we can use the prime factorization method.

Step 1 :

Resolve the given number into prime factors.

Step 2 :

Write these factors in triplets such that all three factors in each triplet are equal.

Step 3 :

From the product of all factors, take one from each triplet that gives the cube root of a number.

Example 1 :

Find the cube root of 512.

Solution :

Hence cube root of 512 is 8.

Example 2 :

Find the cube root of 27 x 64.

Solution :

  =  ∛27 x 64 

We can write 27 as 3 x 3 x  3, like wise 64 as 4 x 4 x 4.

  =  ∛3 x 3 x 3 x 4 x 4 x 4

  =  3 x 4

  =  12

Hence the answer is 12.

Example 3 :

Find the cube root of 125/216.

Solution :

Here we need to find the cube root for a fraction. For that, split the numerator and denominator as much as possible.

  =  ∛125/216

125  =  5 x 5 x 5 and 64  =  4 x 4 x 4

  =  ∛(5 x 5 x 5) /(4 x 4 x 4)

Since we have cube root, we need to take one for each three same terms.

  =  5/4

Hence the cube root of 125/216 is 5/4.

Example 4 :

Find the cube root of -512/1000.

Solution :

Here we need to find the cube root for a fraction. In the cube-root we have negative sign.

Whenever we have negative sign inside the cube root, the answer must have negative sign.

  =  ∛512/1000

512  =  8 x 8 x 8 and 1000  =  10 x 10 x 10

  = - ∛(8 x 8 x 8)/(10 x 10 x 10)

Since we have cube root, we need to take one for each three same terms.

  =  - 8/10

If it is possible, we may simplify

  =  - 4/5

Hence the cube root of ∛-512/1000 is -4/5.

Example 5 :

Find the cube root of 0.027.

Solution :

Here we need to find the cube root for a decimal. 

First let us convert the given decimal as fraction. For that, we have to multiply and divide by 1000.

0.027 x  (1000/1000)  =  27/1000

∛0.027  =  ∛27/1000

  =  ∛(3 x 3 x 3)/(10 x 10 x 10)

  =  3/10

Hence the cube root of ∛0.027 is 3/10.

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