**Cube roots :**

Cube root is inverse operation in finding cubes.

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.

After having gone through the stuff given above, we hope that the students would have understood "Cube-roots".

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