Math, asked by mathursangeeta238, 1 year ago

Find the cube root of 5832 by prime factorization

Answers

Answered by bhakti4616
14

Answer:

18

Step-by-step explanation:

Now, by prime factorisation 5832 can be written as:

5832=2×2×2×3×3×3×3×3×3

Next, we have to group the numbers into three with each group having the same members. Hence we will get:

5832=(2×2×2)×(3×3×3)×(3×3×3)

Now, take one factor from each group, and take cube root of 5832, we will obtain:

5832−−−−√3=2×3×3

In the next step we have to multiply these factors. The number so obtained will be the required cube root. Therefore, we can write:

5832−−−−√3=18

So, we got 5832 as the perfect cube of 18.

Hence, we can say that the cube root of 5832 is 18.

Attachments:
Answered by amitnrw
14

Given : Number 5832

To Find : Cube root of 5832

Solution:

     2           5832

     2           2916

    2            1458

    3             729

    3             243

     3              81

     3              27

    3                9

    3                 3

                       1

5832 = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 3 * 3

= 2³ * 3³ * 3³

= (2 * 3 * 3)³

= 18³

   5832 =   18³

=>  ∛5832 = 18

cube root of 5832  is 18

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