Cube root of 8000 solutions
Answers
Answer:
To find cube root of 8000 by prime factorization method
A number that must be multiplied times itself three times to equal a given number is called cube root
Prime factorization method:
Prime factorization is a number written as the product of all its prime factors.
In order of finding cube root by prime factorization we use the following steps:
Step I : Obtain the given number
Step II : Resolve it into prime factors.
Step III : Group the factors in 3 in such a way that each number of the group is same
Step IV : Take one factor from each group
Step V : Find the product of the factors obtained in step IV. This product is the required cube root
Prime factorization of 8000:
\text{ prime factors of 8000 } = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 prime factors of 8000 =2×2×2×2×2×2×5×5×5
Thus we get,
\sqrt[3]{8000} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5}
3
8000
=
3
2×2×2×2×2×2×5×5×5
Now let us group the factors
\sqrt[3]{8000} = \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{5 \times 5 \times 5}
3
8000
=
3
2×2×2
×
3
2×2×2
×
3
5×5×5
There are 3 groups, so from that group take one factor out
\sqrt[3]{8000} = 2 \times 2 \times 5 = 20
3
8000
=2×2×5=20
Thus cube root of 8000 by prime factorization method is 20
Learn more about cube root by prime factorization method
1) Find the cube roots of the following numbers: (i) -5832
2) Find the cube root of each of the following: (i) -216 x 1728
https://brainly.in/question/4521560
Find the cube root of the following numbers by prime factorization method.
(i) 343
(ii) 729
(iii) 1331
(iv) 2744
Step-by-step explanation:
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Step-by-step explanation:
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