Question

cube root of 21952 by prime factorization

Answer 1

Answer:

The cube root is 28

Step-by-step explanation:

we have to find the cube root of 21952

To find the cube root by prime factorization:

Step 1: Obtain the given number.  

Step 2: Resolve it into prime factors.  

Step 3: Group the factors in three in such a way that each number of the group is same.  

Step 4: Take out one factor from each group obtain in step 3.  

Step 5: Find the product of factors.

This product is the required cube root.  

Number: 21952

After resolving the prime factors, we get

$21952=2\times 2\times 2\times 2\times 2\times 2\times 7\times 7\times 7$

Taking one factor from each group  

$\sqrt[3]{0.008}=2\times 2\times 7=28$

Hence, the cube root is 28

Answer 2

Given:

21952

To find:

find the cube root of the given number by prime factorization method​.

Solution:

First find the prime factors of 21952

prime factors of 21952 = 2x2x2x2x2x2x7x7x7

=> make three groups of same numbers

=> (2x2x2) x (2x2x2) x (7x7x7)

=> 2 x 2 x 7

=> 28

hence, 28^3 is 21952