Find the cube root of 5832 by prime factorization
Answers
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.
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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