Square Root by Prime Factorization
Prime factorization is the process of finding the prime factors of a number, which are the prime numbers that multiply together to make the original number.
To find the square root of a number using prime factorization, you can follow these steps:
Step 1: Prime Factorization: Decompose the given number into its prime factors.
Step 2: Pairing Factors: Pair up identical prime factors in twos.
Step 3: Square Roots of Each Pair: Take one factor from each pair and multiply them together.
Step 4: Multiply Results: Multiply the results from step 3 to find the square root of the original number.
Let’s consider an example for better understanding.
Example: Find square root of 3600 using prime factorization.
Solution:
Step 1: Prime Factorization of 3600:
3600 = 24 × 32 × 52
Step 2: Pairing Factors:
3600 = (2 × 2) × (2 × 2) × (3 × 3) × (5 × 5)
Step 3: Square Roots of Each Pair:
Take one factor from each pair: 2 × 2 × 3 × 5 = 60
Step 4: Multiply Results:
√3600 = 60
So, the square root of 3600 is 60.
Finding Square Root Through Prime Factorization and Repeated Subtraction
Square Root is the one of the many arithmetic operations in mathematics. Square root can be calculated using various methods in mathematics such as long division, prime factorization, repeated subtraction, etc. In this article, we will discuss methods of calculation of square root using prime factorization and repeated subtraction method.
Table of Content
- What are Square Roots?
- Square Root by Prime Factorization
- Square Root by Repeated Subtraction
- FAQs