Find the cube root of the following by prime factorization method 5832 and 21952?

To find the cube root of 5832 and 21952 using the prime factorization method, we first need to factor each number into its prime components.

Finding the Cube Root of 5832

Let's start with 5832:

• Divide by 2: 5832 ÷ 2 = 2916
• Divide by 2: 2916 ÷ 2 = 1458
• Divide by 2: 1458 ÷ 2 = 729
• Divide by 3: 729 ÷ 3 = 243
• Divide by 3: 243 ÷ 3 = 81
• Divide by 3: 81 ÷ 3 = 27
• Divide by 3: 27 ÷ 3 = 9
• Divide by 3: 9 ÷ 3 = 3
• Divide by 3: 3 ÷ 3 = 1

The prime factorization of 5832 is:

2³ × 3⁶

To find the cube root, we take one-third of the powers:

Cube root of 5832 = 2¹ × 3² = 2 × 9 = 18

Calculating the Cube Root of 21952

Now, let's factor 21952:

• Divide by 2: 21952 ÷ 2 = 10976
• Divide by 2: 10976 ÷ 2 = 5488
• Divide by 2: 5488 ÷ 2 = 2744
• Divide by 2: 2744 ÷ 2 = 1372
• Divide by 2: 1372 ÷ 2 = 686
• Divide by 2: 686 ÷ 2 = 343
• Divide by 7: 343 ÷ 7 = 49
• Divide by 7: 49 ÷ 7 = 7
• Divide by 7: 7 ÷ 7 = 1

The prime factorization of 21952 is:

2⁶ × 7³

Taking one-third of the powers gives us:

Cube root of 21952 = 2² × 7¹ = 4 × 7 = 28

Final Results

The cube roots are:

• Cube root of 5832 = 18
• Cube root of 21952 = 28