Question

find the cube root of 8000 by prime factorization method

Answer 1

Cube root of 8000 by prime factorization method is 20

Solution:

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:

$\text{ prime factors of 8000 } = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$

Thus we get,

$\sqrt[3]{8000} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5}$

Now let us group the factors

$\sqrt[3]{8000} = \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{5 \times 5 \times 5}$

There are 3 groups, so from that group take one factor out

$\sqrt[3]{8000} = 2 \times 2 \times 5 = 20$

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

https://brainly.in/question/4902025

Answer 2

Answer:

$\red { \sqrt[3]{8000} } \green {= 20 }$

Step-by-step explanation:

$Resolve \: given \: number \:8000 \: into \\product \:of \:prime \: factors .$

2 | 8000

________

2 | 4000

________

2 | 2000

________

2 | 1000

________

2 | 500

________

2 | 250

________

5 | 125

________

5 | 25

________

**** 5

$8000 =( 2 \times 2 \times 2) \times (2 \times 2 \times 2) \times( 5 \times 5 \times 5)$

$\sqrt[3] {8000} = \sqrt[3] {(2 \times 2 \times 2 )\times( 2 \times 2 \times 2 )\times (5 \times 5 \times 5) }$

$= 2\times 2 \times 5 \\= 20$

Therefore.,

$\red { \sqrt[3]{8000} } \green {= 20 }$

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