Question

find the cube root of 27000 by prime factorization method step by step

Answer 1

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Answer 2

Given: A number 27000

To find: Cube root of the given number using Prime Factorization

Solution: According to the given question,

The given number is 27000

Step 1: Start dividing 27000 by the lowest prime number until it is completely divided and the final quotient is also a prime number.

Step 2: Express the number as the product of it's prime factors.

Using Prime Factorization, 27000 can be expressed as:

27000 = (2 × 2 × 2) × (3 × 3 × 3) × (5 × 5 × 5)

Step 3: Take one number from each group of 3 identical numbers. Find their product. The resulted number is the cube root.

$\sqrt[3]{27000}$ = 2 × 3 × 5 = 30

Hence, the cube root of 27000 is 30.