Finding Square Roots with Prime Factorization - Easy Guide

Welcome to understanding prime factorization with Spark.E!Before we dive into prime factorization, let's understand what prime numbers are.Here are some examples of prime numbers. Notice how each can only be divided by one and itself.Prime factorization is the process of breaking down a number into its prime building blocks.Let's use seventy-two as an example. We'll create a factor tree to break it down into its prime factors.First, we find any two numbers that multiply to give seventy-two. Let's use eight and nine.Eight can be broken down into two and four.Nine breaks down into three times three.Finally, four breaks down into two times two.Now we can write seventy-two as a product of its prime factors: two times two times two times three times three.In the next section, we'll learn how to use these prime factors to find square roots!Let's continue our journey into prime factorization!To determine if a number is a perfect square, we need to examine its prime factors in pairs.Let's look at seventy-two. We can write it as two times two times two times three times three.Let's try to pair up these factors. We can make one pair of twos...And another pair of twos...But we have one two left over without a pair...Our threes form a nice pair.Let's count the appearances of each prime factor.Since two appears an odd number of times, seventy-two cannot be a perfect square.Now let's look at one hundred forty-four. We can write it as two times two times two times two times three times three.Here we can pair up all our twos evenly...And our threes also form a perfect pair.Let's count the appearances of each prime factor in one hundred forty-four.Since all prime factors appear an even number of times, one hundred forty-four is a perfect square.This gives us our rule for perfect squares: all prime factors must appear an even number of times.